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 fl CaKIPUTEH-flSSJSTED 
 PLfiNNJNG METHOD FQR 
 JMDANDUfll. FARMS 
 
 
 F ILLINOIS 
 LIBRARY, 
 
 I. W. MARCEAU C. B. BAKER 
 
 R. E. TONGATE JOHN T. SCOTT, JR. 
 
 THE LIBRARY OF THE 
 
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 University of Illinois at Urbana-Champaign / College of Agriculture / Special Publication 20 
 
fl COMPUTER-ASSISTED 
 Pl.flWMJWE HJETHQD FOR 
 INDIWDUflL FfiRiriS 
 
 I. W. MARCEAU 
 R. E. TONGATE 
 
 C. B. BAKER 
 
 JOHN T. SCOTT, JR. 
 
 Special Publication 20 
 
 University of Illinois at Urbana-Champaign 
 
 College of Agriculture 
 
 February, 1971 
 
This publication was written by I. W. MARCEAU, Research 
 Assistant Professor of Computer Science, University of 
 Illinois; R. E, TONGATE, Assistant Professor of Agricul- 
 tural Economics, Ohio State University; and C. B. BAKER 
 and JOHN T. SCOTT, JR., Professor and Associate Pro- 
 fessor, respectively, of Agricultural Economics, University 
 of Illinois. Much of this report is based on the research 
 reported by I. W. Marceau in Linear Programming for 
 Individual Farms: A Contribution Toward a Commercially 
 Applicable System, Ph.D. thesis, University of Illinois, 
 1968; by R. E. Tongate in A Cost-Reducing System for 
 Applying Linear Programming Models to Planning Prob- 
 lems of Individual Farms, Ph.D. thesis, University of 
 Illinois, 1969; and by C. B. Baker, J. T. Scott, Jr., and 
 R. E. Tongate, Data Requirements and Costs Associated 
 with Programming for Individual Farms, final report to FS 
 Services, Inc., 1968. The section dealing with the field 
 test is based on work done by R. E. Tongate while a 
 Research Associate in the Department of Agricultural 
 Economics, University of Illinois. The research for this 
 report was supported in part by a grant from FS Services, 
 Inc., Bloomington, Illinois. 
 
CONTENTS 
 
 The Problem 1 
 
 A Planning Method 3 
 
 A Field Test of the Method 9 
 
 Results and Conclusions 13 
 
 Appendix 1: The Generalized Linear 
 
 Programming Model 20 
 
 Appendix 2: The Matrix Generator 
 
 and Report Generator 24 
 
 Appendix 3: An Example of a 
 
 Crop Production Run 28 
 
The Problem 
 
 Stimulated by the rapid advances in electronic data processing, 
 agricultural economists have become interested in adapting modern 
 decision theory to practical farm management problems of individual 
 farms. Linear programming, the most widely used modern decision tool, 
 is still the most versatile of the available advanced decision techniques. 
 Its use in farm planning, however, has been confined mainly to re- 
 search. Commercial applications to individual farms have so far had 
 little success. We shall discuss some of the reasons for this lack of 
 success and examine some alternatives in planning methods that may 
 facilitate applying linear programming to farm planning. 
 
 Regardless of the decision tool to be employed, the principal choice 
 in problem-formulation is between the whole-farm and the sub-farm 
 conceptions of problems to be solved. Because all components of the 
 firm are economically related, using the whole-farm approach facilitates 
 specifying an objective to be attained. To single out one component 
 necessitates an artificial partitioning that can cause serious problems 
 both in logic and in practice. The disadvantage of the whole-farm ap- 
 proach, however, is the size of the model necessary to represent a firm 
 in sufficient detail to provide useful answers to practical questions. 
 
 The major factor in past failures of a whole-farm approach has 
 been the high cost of preparing a model applicable to a specific in- 
 dividual farm. Because programming for individual farms has been 
 so uneconomical, there has in some cases been a return to the use of 
 "representative" farms. This approach has been notably unsuccessful in 
 the past and appears limited in any future extension use because of 
 the difficulty of relating an optimal solution for a "representative" farm 
 to the real-world situation on a specific farm. The problem lies in 
 explicitly taking account of the very real differences between individual 
 farms and some "average" of them. 
 
 To be commercially successful, the planning consultant must pro- 
 vide a service at a price sufficiently high to yield a "reasonable" profit 
 but low enough to attract the cost-conscious farmers who are his 
 potential clients. He must also utilize a model complex enough to 
 provide relevant analyses. As a partial solution, costs must be reduced 
 in some or all of three areas: data collection, data use, and interpretation 
 of results. 
 
 Data collection. Because of the time and skills required of the data 
 collector, the cost of acquiring data relevant for farm planning will 
 remain high. Furthermore, although much data can be obtained from 
 farm records at almost zero marginal cost, data collection costs remain 
 high because many items required in forward planning either are not 
 collected with the traditional farm records or are essentially lost in 
 
2 The Problem 
 
 the usual summarization processes used with record systems. Most 
 major farm record systems are oriented primarily toward the collection 
 and analysis of financial information used to prepare tax and deprecia- 
 tion schedules and to permit interfarm comparisons of the past perfor- 
 mance of the individual farmers. These record systems are thus highly 
 oriented toward collecting accounting data, with little attempt made to 
 collect information directly relevant to forward planning. 
 
 Data use. The major cost in data use is not the computer time 
 required to solve a linear programming problem but the time and 
 skill necessary to define and prepare a model for an individual farm and 
 to keypunch and verify the data cards required for input. In a conven- 
 tional system, all non-zero matrix coefficients must be entered on cards. 
 Up to 10,000 cards may be required to input a farm model, which 
 must first have been defined by a skilled worker. The card punching 
 and verifying for such a model requires about 30 man-hours. When 
 added to the costs of model formulation, these costs make the use 
 of linear programming for individual- farm planning prohibitively 
 expensive. 
 
 Interpretation of results. The solution to a linear programming 
 routine usually consists of coded lists of variables and activity levels in 
 a form that is not suitable for use by extension personnel or farmers. 
 It is necessary, therefore, to interpret such solutions and present them in 
 a form easily understandable by field personnel. The conventional ap- 
 proach has been to use clerical help to "decode" the solutions and extract 
 the information relevant to the farmer, presenting it in some form of 
 report. This procedure, besides being inefficient, is expensive and subject 
 to transcription errors. 
 
 Object of the Study 
 
 The overall objective of this study has been the development of a 
 commercially viable linear programming system for use in individual- 
 farm planning. Our research effort has been concentrated on reducing 
 the costs discussed above, particularly the costs of data use and solution 
 interpretation. The problems of data collection, however, are such that 
 little cost reduction appears likely in the near future. 
 
 In the method we shall propose, the whole- farm approach to plan- 
 ning is used. This is made feasible by the efficient design of a general 
 model and by the development of matrix-preparation and report-w r rit- 
 ing procedures, which greatly reduce the costs of individual- farm 
 programming. By adopting the whole-farm approach, we do not deny 
 the likelihood of success with models that deal with sub- farm problems. 
 Indeed, it seems likely that useful planning service will consist of a 
 whole-farm planning system backed by a set of special-purpose models 
 designed to provide sophisticated solutions to sub-farm problems. 
 
 
A Planning Method 
 
 Generalized Models 
 
 Using an "average" model has the cost-reducing advantage of using 
 one model for many farms. Our objective has been to develop a model- 
 ing technique that provides benefits analogous to those from an 
 "average" model but also permits the structuring of models tailored 
 for each of the individual farms to be planned. The most general and, 
 it presently appears, the most satisfactory approach has been to develop 
 a model for each defined type of farm, where a farm "type" means 
 a class of farms with certain resource characteristics and realistic pro- 
 duction alternatives. A general model, the "crop-livestock model," has 
 been structured and tested for farms producing field crops, swine, and 
 fed cattle. 
 
 This model is general in the sense that its structure comprises a 
 comprehensive set of production and marketing alternatives. It is short 
 run in the sense that alternatives are described in terms of annual re- 
 turns, requirements, and costs. A model can be tailored to an individual 
 farm by first selecting the subset of production alternatives and con- 
 straints that represent both the physical and subjective characteristics 
 of the farm and then entering those coefficients that are specific to the 
 farm, such as objective function values, constraint levels, crop yields, 
 and labor requirements for production activities. 
 
 The generalized model currently in use comprises 1,840 activities and 
 477 constraint rows. The crop production section allows up to 10 
 crop growing activities, each with as many as six technological levels 
 (fertilizer, row spacing, tillage practices, etc.), on as many as 20 fields. 
 A "field" may refer to any physical division of the land area. Crop 
 production on lands rented from various landlords under varying 
 leasing arrangements can be considered by treating the crop alternatives 
 on land from each source either as different crops or as different levels 
 of the same crop. The varying divisions of costs and returns under 
 alternative leasing arrangements can be reflected in the objective func- 
 tion and crop yield coefficients. The alternatives of entering or not 
 entering government programs can also be satisfactorily considered for 
 any given farm, within the structure of the general model, because 
 differentials in guaranteed prices under varying levels of participation 
 can be reflected by considering the participation levels as different crops. 
 
 The crop disposal section of the model consists of a crop storage 
 activity and 12 monthly selling activities for each crop. All crops are 
 regarded as potential stock feed, so 12 monthly activities are provided 
 for feeding each crop to cattle and 12 for feeding to swine. If a particu- 
 lar crop number in the model is assigned to a crop that is not a stock 
 feed, the feeding option is not provided when the individual-farm 
 matrix is set up. 
 
4 A Planning Method 
 
 The livestock section of the model consists of eight sets of both 
 cattle feeding alternatives and swine farrowing and feeding alternatives. 
 These allow the consideration of various types of livestock classed by 
 weight, feeding period, rate of gain, sex, etc. Each set includes 12 
 activities differentiated by the month of start. The swine activities can 
 be used to specify farrowing and swine feeding activities, with farrow- 
 ing or feeding starting in any month. Livestock feed requirements are 
 met by crops produced on the farm or by purchased f eedstuffs. Up to 20 
 feedstuffs can be purchased, with the restriction that all feeds purchased 
 must be fed to livestock. No grain trading is permitted. 
 
 The constraints of the model are the area of land in each field, the 
 hours of labor available during each month, the storage facilities avail- 
 able for crop products, the limitations imposed on crop acreages by 
 government programs or crop rotations, the feedlot facilities for cattle 
 and swine, the farrowing facilities for swine, and the monthly nutrient 
 requirements for cattle and swine. Xo attempt has yet been made to 
 include financial components in this model. 
 
 The generalized model was developed to reduce the costs of prepar- 
 ing individual- farm models by providing a framework within which 
 a model for a specific farm could be structured. 1 Activity units of the 
 general model are so defined as to reduce to unity as many as possible 
 of the non-zero coefficients required to structure a farm model. To 
 further reduce the entry of coefficients required for individual-farm 
 models, the nutrient requirements for livestock of various types, classi- 
 fied by body weight and daily rates of gain, are tabulated and stored 
 in a form accessible to the matrix-preparation procedure. The nutrient 
 content of a wide range of livestock feeds has been similarly tabulated 
 and stored. It is assumed that the nutrient content of feedstuffs does not 
 vary significantly between sources of supply; this does not imply, how- 
 ever, that nutrient characteristics of feeds on individual farms will not 
 be utilized if they become available. 
 
 The quantity of additional data needed to specify a model for an 
 individual farm has thus been reduced to those items characterizing 
 the unique properties of the farm: yields, labor requirements for crop 
 and livestock production, constraint levels, and coefficients of activity 
 units in the objective function. 
 
 A System for Utilizing Generalized Models 
 
 After all the constraints and activities have been specified, the 
 linear programming tableau must be constructed. In past applications 
 of linear programming to individual-farm decision problems, first a 
 model is developed and then the tableau is formed manually. We have 
 
 1 The general model structure is described in Appendix 1. 
 
A Planning Method 5 
 
 investigated having the computer do most of the tedious and costly 
 work of preparing the tableau by matrix generation, using a specially 
 written matrix-generator routine. Under parameter control, the routine 
 generates and stores in memory any subset of the constraints and ac- 
 tivities of the general model required to specify an individual-farm 
 matrix. In our method the individual-farm data are card-input during 
 matrix generation. The tabulated secondary data (nutrient require- 
 ments of livestock and nutrient contents of feeds) are stored in arrays 
 embedded in the matrix-generator code. 
 
 The matrix-generator routine generates the individual farm matrix, 
 which consists of a subset of the activities and constraints defined in the 
 general model. The relevant activities and constraints for a particular 
 farm are specified by parameters on the input cards read by the matrix- 
 generator routine. These parameters specify the crop-growing, live- 
 stock-raising, crop-disposal, and feed-source alternatives. Only the 
 columns corresponding to the activities specified and the rows cor- 
 responding to the relevant constraints are generated for a particular 
 farm matrix. The unit coefficients and the secondary data associated 
 with these various activities are automatically entered into the appro- 
 priate locations of the matrix. 2 Individual-farm data input on cards 
 read with the parameter cards are also placed in the appropriate matrix 
 cells. Thus, the punched card input required to structure an individual- 
 farm linear programming model consists of a series of parameters 
 specifying the production alternatives to be considered and containing 
 the specific data for the farm (See Appendix 2). The completed matrix 
 is then passed to the linear programming code for solution. 
 
 The matrix generator is designed to handle "batched" data. The 
 number of farms that can be run together depends only on the limita- 
 tions imposed by the size of the computer memory. 
 
 Our matrix-generator routine is written in FORTRAN IV for the 
 IBM 360/75 at the University of Illinois. The linear programming 
 code used is the IBM MPS/360 package. The crop and livestock vec- 
 tors included make the matrix generator applicable to a wide range 
 of farm conditions in Illinois and in the Corn Belt generally. Accom- 
 modating vectors relevant to other alternatives such as milk or beef 
 calf production, however, would require not only modifying the linear 
 programming model, but also altering the matrix-generator routine. 
 
 The costs of solution interpretation have been significantly reduced 
 by using a report-generator routine, which sorts from the linear pro- 
 gramming solutions the items that are relevant to the decision maker 
 
 2 The unit coefficients apply to all farms and can therefore be placed in the ap- 
 propriate matrix locations during matrix generation. The required arrays of 
 secondary data are entered into appropriate locations of the matrix when called 
 for by a parameter. 
 
6 A Planning Method 
 
 .and outputs them in easily understood terms. The report generator 
 currently prepares two reports. Report I, the Production Plan, shows 
 the recommended acreages and technological levels of each crop by 
 field ; the numbers of each type of feeder cattle, purchase and sale time, 
 weight, and optimal rate of gain; and, for swine, a similar feeding plan 
 plus a farrowing time-table. The least-cost feed mix, utilizing both 
 grown and purchased feeds, is presented on a monthly basis for both 
 cattle and swine. Report II is the expected budget for the farm, pre- 
 sented as a summary of expected costs and returns for each crop and 
 type of livestock. A planned third report will contain a constraint and 
 activity analysis and will list the amounts of resources unused, the 
 shadow prices of the constraining resources, and the results of para- 
 metric programming when required. 
 
 The Production Plan and Budget are illustrated and discussed in 
 the output of the sample problem presented in Appendix 3. Figure 1 
 is a flow diagram of the whole system. 
 
 Timing of Runs 
 
 The timing of the short term production planning runs for in- 
 dividual farms must coincide with the period during which the plan- 
 ning decisions are made by the farmer. For Midwest crop-livestock 
 farms, for example, crop production should be planned initially in the 
 fall, with perhaps an updated plan in early spring to take account of 
 any changes in production costs or projected product prices. 
 
 Since any decision on the allocation of the limited resources of 
 land and labor among cropping alternatives must take account of the 
 potential disposal of the crops produced, price projections must be 
 made for the disposal alternatives — sale at harvest, sale from storage, 
 and use as livestock feed. Sale prices of crop products are estimated 
 for up to 24 months in advance, and livestock purchase and sale prices 
 for up to 32 months in advance. The additional months allow any live- 
 stock entering the plan in the last months of the disposal year (months 
 13 through 24) to be fed out. 
 
 The length of the price projection period necessitates updating the 
 price estimates on which crop disposal and livestock feeding plans are 
 based. Therefore, a "crop disposal" run should be made during the 
 September that follows the production plan for the current crop. By 
 this time, the vagaries of weather will have affected the crops, and 
 the uncertainty of yields will have been reduced. The yield estimates 
 are then updated and a disposal plan is run using new 12-month price 
 estimates for the crop products and 18-month estimates for livestock. 
 The disposal and livestock sections of the farm plan are thus re- 
 optimized, using price estimates that should be more reliable because 
 they are projected for a shorter period. 
 
A Planning Method 
 
 INDIVIDUAL 
 FARM DATA 
 
 INDIVIDUAL 
 
 FARMER 
 
 PREFERENCES 
 
 
 SECONDARY 
 DATA STORAGE 
 
 MATRIX 
 GENERATOR 
 
 REPORT I 
 
 PRODUCTION 
 
 PLAN 
 
 IBM 360/MPS 
 SYSTEM 
 
 REPORT 
 GENERATOR 
 
 REPORT II 
 FARM BUDGET 
 
 \ 
 
 report iii 
 
 [activity 
 
 •analysis 
 
 Flow diagram of the "new" system for programming individual farms. 
 
 (Fig. 1) 
 
 The amount of labor available for livestock feeding in the 12 months 
 following harvest of the current crops is limited to the total labor avail- 
 ability less the amount projected to be used for producing the next 
 mix of crops, which will be grown concurrently with the disposal period 
 of the previous crops. The projection for labor use for the next crop 
 production period is assumed to be equal to the total periodic labor use 
 for all crops in the previous production year, although the mix of crops 
 and cropping practices may differ. 
 
8 A Planning Method 
 
 Later in the fall, the next crop production plan is produced, with 
 labor constraints adjusted by the amounts used to feed livestock in the 
 crop disposal period. Since the crop disposal period lasts only until 
 harvest of the crops currently being planned, some livestock will re- 
 main in the system at the end of this arbitrarily defined period. These 
 livestock are entered in the (then) current crop production model as 
 inventories. As such, they may influence the choice of crops to be 
 grown. At the time of the next crop disposal run, these livestock will 
 already be in the feedlot and must be fed out, so they are entered in 
 the new crop disposal run as an inventory. 
 
 Thus, the planning system is dynamic in the sense that it allows 
 continual overlap between the discrete planning periods and continual 
 updating of information on prices and costs. At each successive run, 
 decisions to which the farmer is already committed are treated as fixed, 
 with relevant quantities entered in the next run as inventories. 
 
 
A Field Test of the Method 
 
 Innovating a computerized planning system requires a procedure 
 that is not only free of logical error but also economically feasible. 
 That is, the results of the system must be valued by the farmer at a 
 level that exceeds their production costs by an amount sufficient to 
 attract the resources of a planning agency. A pilot study was organized 
 to evaluate the system's economic feasibility and to test its workability 
 when operated outside of laboratory-like conditions. 
 
 We were also interested in the educational effects on the farmers 
 who applied the planning system in the pilot study. Since our model 
 constructs alternatives over the entire range of farm organization, we 
 would expect the user's understanding of whole- farm interrelationships 
 to improve. By seeing direct illustrations of the value of input data, 
 the user might more fully appreciate the usefulness of accurate and 
 relevant planning information. Finally, we hoped the study would 
 illustrate that computerized planning is, like other approaches, but one 
 among many systematic ways to explore the effects of alternatives. It 
 provides no magic solutions ; yet it can efficiently consider a wide range 
 of alternatives complexly interrelated with a farmer's goals and the 
 limitations of his resources. 
 
 Conduct of the Test 
 
 Selection of test farms. Limited resources confined the study to 
 only 10 farms. No attempt was made to represent any population of 
 farms with a probability sample. Instead, farmers were chosen from 
 among volunteers from Illinois Farm Business Farm Management 
 Associations on the basis of geographic dispersion, varied resource 
 conditions, and market environment in which to test the properties of 
 the planning system. Information about the study was distributed to 
 Association fieldmen, who helped us select and work with the chosen 
 farmers. 
 
 Diversity of farm type was sought, subject of course to limitations 
 imposed by properties of the planning model. Thus, crops, cattle feed- 
 ing, and hog farrowing and feeding were considered. Since these 
 alternatives are the ones common to the great majority of farms in 
 Illinois, these properties of the model were not especially confining. We 
 also tried to include diverse sizes of enterprises. 
 
 It would have been desirable to have tested the system with opera- 
 tors who displayed a wider range of managerial skills. By confining the 
 choice to cooperators in the Farm Business Farm Management Asso- 
 ciation, however, the range of variation was limited, because most 
 operators were doubtless somewhat above the average in management 
 skills; the total population of commercial farmers in Illinois might be 
 
10 A Field Test of the Method 
 
 expected to show more variation. Their membership in the Association 
 did, however, assure a known basis of data from farm records. 
 
 Finally, it was essential that the chosen farmers be interested 
 enough in the study to cooperate fully in providing data for the planning 
 model and in taking time to understand its properties and its results. 
 A small fee ($50) was charged each farmer chosen for the study. The 
 fee did little more than defray some of the travel costs incurred, yet it 
 gave the cooperator a real stake in the study and in its relation to his 
 own operation. 
 
 Of the 10 farms selected, two were located in Douglas County, 
 three in McLean County, three in Sangamon County, and two in Will 
 County. For reasons similar to those already mentioned, there was less 
 representation of small farms than might have been desirable. Al- 
 though the variation in size was fairly wide, from 382 to 1,229 tillable 
 acres, averaging 737 acres, all farms were relatively large. Five farms 
 reported cattle, averaging 239 head per farm. Six farms reported hogs, 
 averaging 840 head per farm. For all 10 farms, an average of 2.4 men 
 were employed per year per farm, including all full-time and part-time 
 help. 
 
 Computation and consultation. As already outlined, the planning 
 system is designed for two runs per year — a "production" run and 
 a "crop disposal" run. The crop production plan is to be prepared in 
 the fall or in February or March, prior to planting time; it provides a 
 cropping plan by field and technological level. A tentative disposal plan 
 is also usually presented at this time. The pilot study was organized 
 too late to provide a production plan to cooperating farmers before 
 they had already made their decisions for the 1969 crop. Instead, this 
 first run was used primarily to locate any modifications needed in the 
 generalized model and to acquaint the cooperating farmer with the 
 planning process. In short, the crop production run was a "dry run" 
 with respect to planning the 1969 crop, though of course implications 
 could be drawn for 1970 and subsequent years. At any rate, data 
 were collected in March and April for 1969 crop production. On-the- 
 farm interviews yielded estimates of constraint values, production 
 alternatives, and available machinery and equipment. At the office, 
 records were analyzed and secondary data were adjusted to complete 
 the assemblage of input data for the planning model. 
 
 Data collection and preparation represented by far the most difficult 
 problem encountered during the pilot study. Farmers did not keep 
 records in sufficient detail to yield coefficients such as cash costs per 
 unit or labor requirement coefficients for individual enterprises. As a 
 result, these detailed items had to be estimated with the farmer, a very 
 time-consuming process. Even more time was required to collate the 
 data in the office. In addition, well-trained interviewers were required 
 
A Field Test of ttie Method 11 
 
 because a large quantity of secondary data from present records sys- 
 tems had to be adjusted to reflect the particular farm's coefficients. 
 Because the accuracy of coefficients thus obtained was somewhat du- 
 bious, solutions had to be interpreted with a high degree of caution and 
 uncertainty. It will probably never be possible to obtain coefficients that 
 are completely accurate for a particular farm, but it is desirable to 
 have coefficients that are more reliable than those presently used. 
 
 Given the timing of the pilot study, it was possible to compare the 
 crop production plan with the plan currently being followed on a farm. 
 An explanation of any major differences usually involved tracing the 
 programmed solutions back to the initial data to determine the em- 
 pirical basis for the differences. Relevant estimates of coefficients were 
 always reviewed at this point to determine if differences w r ere due to 
 data errors ; if so, the model was rerun. When the farmer could agree 
 with the accuracy of the coefficient estimates, he was asked if the 
 solution made sense to him. 
 
 By this point, the farmer commonly asked what would happen if 
 one or more coefficients varied from w 7 hat was input in the model 
 specification. Often he was interested in the effects of alternative plans 
 he was considering for the use of his resources. Most farmers, for 
 example, wanted to know w r hether or not the government Feedgrains 
 Program should be followed. 
 
 At this level of his understanding, we could now emphasize the 
 potential value of multiple runs. The farmer was encouraged to select 
 three or four alternatives he would like most to be investigated in the 
 crop disposal run yet to be made; to describe these alternatives in 
 writing; and to have them, along with any questions, available for the 
 investigator's return visit to the farm in August just before the final 
 runs. The farmer was also requested to review closely the cost and 
 labor coefficients before the final run was formalized. His appreciation 
 of the importance of this review clearly was heightened by the under- 
 standing he gained when the crop production run was interpreted. 
 
 The third visit, in August, was the shortest of the farm visits. Most 
 procedural questions had already been answered; the alternatives to be 
 considered had already been discussed ; updating the data, preparatory 
 to the 1969 crop disposal and the 1970 crop production runs, was thus 
 accomplished rather easily. 
 
 The number of crop disposal and crop production runs varied from 
 as few as three to as many as six per farm. Some farmers suggested 
 alternatives that involved investment decisions instead of shortrun 
 decisions. The investigator explained the limitations of the one-period 
 model for evaluating such decisions, but proceeded to do what could be 
 done in exploring the effects of alternative investments. For example, 
 investments that would alter a constraint quantity or a technical coeffi- 
 
12 A Field Test of the Method 
 
 cient could be examined for their effects on organizational choices and 
 on annual profits. These effects, in turn, could be compared with the 
 farmer's estimate of costs of making the investments. 
 
 The solutions in the crop disposal run detailed optimal actions for 
 disposing of the 1969 crop and for planting the 1970 crops. All solu- 
 tions were returned before October 1 since, to be relevant for current 
 decisions, they had to be in the hands of the farmer before time for 
 silage cutting, soybean and corn harvesting, fall plowing and fertilizing, 
 and wheat sowing. The format for the crop disposal solution was the 
 same as for the preceding crop production solution, so considerably less 
 time was required to explain the output from this run. 
 
 At least three alternatives were explored for each farm by means of 
 multiple runs. Most of the time spent in the final farm visit was used 
 to analyze the differences between these various runs. After all runs 
 had been discussed, the farmer invariably expressed concern with the 
 general implications for his particular farm. Was he on the right track ? 
 Did the programmed results imply significant changes in direction of 
 production? Should he seriously consider changing his combination 
 of enterprises or the volume of business in any of the enterprises? 
 
Results and Conclusions 
 
 Cost Comparisons for Individual Farm Programming 
 
 To show the cost reductions resulting from this system, we compare 
 the costs incurred by the matrix-generator/report-generator system 
 (henceforth called the "new" system) with those of the "conventional" 
 method. 1 Table 1 lists the tasks involved in each method. The cost 
 
 Table 7. — Tasks Required for Individual Farm Planning 
 
 Conventional system 
 
 New system 
 
 One-time setup of: 
 
 a. general model structure 
 
 b. tables of secondary data 
 
 2. Acquisition of individual-farm data 
 (farm interview) 
 
 3. Preparation of data for input into the 
 L.P. tableau; includes determining 
 appropriate secondary data 
 
 4. Matrix preparation — complete the 
 linear programming tableau 
 
 5. Identification of data on keypunch 
 forms 
 
 6. Keypunching and verification of all 
 non-zero matrix coefficients 
 
 7. Solution of problem 
 
 8. Organization of solution into a form 
 understood by farmer 
 
 9. Return of solution to farmer 
 
 1. One-time setup of: 
 
 a. general model structure 
 
 b. matrix-generator routine 
 
 c. report-generator routine 
 
 d. secondary data arrays within ma- 
 trix generator 
 
 2. Acquisition of individual-farm data 
 (farm interview) 
 
 3. Preparation of data for input into the 
 L.P. tableau; includes determining 
 appropriate secondary data 
 
 4. Matrix generation 3 
 
 5. Coding of parameters and data on 
 coding forms 
 
 6. Keypunching and verification of in- 
 dividual-farm data and matrix-gener- 
 ator parameters 
 
 7. Solution of problem 
 
 8. Report generation 
 
 9. Return of solution to farmer 
 
 a Not performed in this order; performed by the computer just prior to solution. 
 
 comparisons are concerned only with the direct costs incurred in using 
 an established system; one-time setup costs are not shown, since these 
 should be considered not as direct costs but rather as an investment to 
 be amortized over time by a commercial farm planning service. Simi- 
 larly, indirect or overhead costs are not shown but must of course be 
 taken into account by a service organization. 
 
 1 The "conventional" method utilizes a standard matrix structure of the same 
 type as the general model of the "new" system but requires manual preparation 
 of the input matrix and manual interpretation of solutions. In addition, secondary 
 data are tabulated in a convenient form, but their input is manual rather than 
 automated. 
 
 13 
 
14 Results and Conclusions 
 
 The cost analysis is based upon the following general assumptions: 
 
 1. The individual farm planning service is offered by a firm that 
 has programmed several hundred farms ; therefore, efficient procedures 
 have been developed for performing all tasks for both methods. 
 
 2. A staff of sufficient size and training is available to perform all 
 tasks. 
 
 3. Staff members are efficiently utilized by the planning organiza- 
 tion throughout the year even though the farm planning service will be 
 seasonal. 
 
 4. Exactly the same data are needed for both methods, including 
 secondary data such as prices and costs, which have been calculated 
 and tabulated in an accessible form. 
 
 5. Exactly the same model structure is used in both methods. 
 
 6. Only two farm visits are required: one to collect the data and one 
 to return the solution. 
 
 7. The work is performed by employees with different levels of 
 skills; the more highly skilled (the farm interviewer) makes $5.50 per 
 hour, and clerical help receives $3 per hour. 
 
 8. Computer time is priced at $8 per minute. 
 
 9. All time and cost estimates are based upon actual experience but 
 are adjusted to reflect economies expected due to volume and experience. 
 
 10. Direct costs (Table 2) are the total for both the "crop disposal" 
 and "crop production" runs, since data for both are collected in one 
 farm visit and results of both are interpreted during one farm visit. 
 
 Data collection cost. Table 2 shows the direct costs of operating 
 the "conventional" and the "new" systems. Data collection costs are the 
 same for both methods, since the procedures discussed above must be 
 implemented before cost reductions actually occur. The estimated data 
 collection and preparation costs for both methods is §77. 
 
 Matrix preparation costs. After the appropriate production alter- 
 natives and constraints have been specified — that is, the model for- 
 mulated for a particular farm — 20 to 25 man-hours are required to 
 manually prepare a matrix for an average farm. The interviewer is 
 needed for only about three hours of this time; the remaining work 
 can be performed by clerical help. Then, because it is usually too 
 difficult to punch cards directly from the matrices themselves, 8 to 12 
 hours are required to copy the coefficients and their identification 
 (by row and column) onto the forms from which the input is punched 
 for the MPS/360 linear programming routine. In the conventional sys- 
 tem, 4,000 to 10,000 data cards must be punched and verified for an 
 average farm. Matrix preparation, coding, punching, and verification 
 cost approximately $203 for an average farm, using conventional 
 procedures. 
 
Results and Conclusions 
 
 15 
 
 Table 2. — Direct Costs of Alternate Systems, by Tas/c a 
 
 Conventional system 
 
 New system 
 
 1. Zero operational cost 
 
 2. 6 man-hours to interview for individ- 
 ual farm coefficients @ $5.50 per hr. 
 = $33.00 
 
 3. 8 man-hours to adjust and organize 
 data @ $5.50 per hr. = $44.00 
 
 4. 23 man-hours to prepare the L.P. 
 tableau — 3 hrs. @ $5.50 per hr. and 
 20 hrs. @ $3.00 per hr. = $76.50 
 
 5. 10 man-hours to enter data on key- 
 punch forms for keypunching @ $3.00 
 per hr. = $30.00 
 
 6. 16 man-hours to keypunch and ver- 
 ify data (6,000 cards) @ $6.00 per hr. 
 = $96.00 
 
 7. Solution time of 6}4 minutes @ $8.00 
 permin. = $52.00 
 
 8. 14 man-hours to interpret solution @ 
 $3.00 per hr. = $42.00 
 
 9. 5 man-hours to return solution to 
 farmer @ $5.50 per hr. = $27.50 
 
 Total Direct Cost = $401.00 
 
 1. Zero operational cost 
 
 2. 6 man-hours to interview for individ- 
 ual farm coefficients @ $5.50 per hr. 
 = $33.00 
 
 3. 8 man-hours to adjust and organize 
 data @ $5.50 per hr. = $44.00 
 
 4. One minute computer time @ $8.00 
 per min. = $8.00 
 
 5. 2 man-hours to code parameters and 
 data on coding forms @ $5.50 per hr. 
 = $11.00 
 
 6. 1 man-hour to keypunch and verify 
 data (150 cards) @ $6.00 per hr. = 
 $6.00 
 
 7. Solution time of 6K minutes @ $8.00 
 per min. = $52.00 
 
 8. Yi minute computer time for report 
 generation @ $8.00 per min. = $4.00 
 
 9. 5 man-hours to return solution to 
 farmer @ $5.50 per hr. = $27.50 
 
 Total Direct Cost = $185.50 
 
 a The tasks are those listed in Table 1. 
 
 In the new system, approximately two hours are required to code 
 parameter and data cards for an average farm. Since the total number 
 of cards necessary for the two runs has been reduced to approximately 
 150, only about one hour is required for keypunching and verification. 
 The computer takes about one minute to generate the matrix. Thus, 
 in the new system, matrix preparation, coding, keypunching, and 
 verification cost approximately $25 for an average farm. 
 
 Interpretation costs. Using the conventional procedure, trained 
 personnel must interpret and reorganize the solution into a meaningful 
 report. The numeric code names used for identification in the computer 
 must be translated into names of activities understandable to the 
 farmer, which means constant reference to the original list of activities 
 and constraints. This process is very time-consuming (hence costly), 
 even for trained personnel: 12 to 15 hours are required to decode, re- 
 organize, and make the calculations necessary for the four reports 
 suggested in this study (a budget and a production plan for each run). 
 In addition, about five hours are required to interpret the solutions to 
 the individual farmer. This means the total cost of solution interpreta- 
 tion in the conventional method is approximately $70. 
 
16 Results and Conclusions 
 
 The report-generator routine developed during our study uses the 
 computer to carry out the task of report preparation. Approximately 30 
 seconds of computer time is required; clerical time is eliminated en- 
 tirely. However, interpretation to the farmer still takes the same five 
 hours as in the conventional method. The total cost of interpretation 
 in the new system is about $32. 
 
 Solution costs. The solution time required by the computer is 
 exactly the same under both systems, although it will of course vary 
 from farm to farm, depending upon the number of constraints and 
 production activities considered. The average solution time for farms 
 in the pilot study was about 6)/2 minutes. Assuming a computer cost of 
 $8 per minute, solution costs are about $52. 
 
 Total direct costs for the new system ($185.50) are less than half 
 of those for conventional procedures ($401). Thus the new system 
 significantly reduces the direct cost of individual- farm programming. 
 
 Other costs. A commercial firm would incur and have to cover 
 setup and overhead costs in addition to direct costs. Setup costs can 
 vary substantially, depending upon the type of firm undertaking the 
 effort, the personnel of the firm, and the type and detail of the planning 
 service. It is difficult here to estimate an average setup cost, as this 
 could range from a few thousand dollars to more than $100,000. De- 
 veloping appropriate computer programs thus involves a major initial 
 investment, but this is the only way of lowering the variable (and aver- 
 age) cost of computerized management services to farmers to an ac- 
 ceptable level. Overhead costs per farm would vary considerably with 
 such factors as the volume of business. However, a planning service 
 utilizing a system similar to the one developed here could probably ex- 
 pect to incur overhead costs of approximately 75 to 100 percent of the 
 direct costs. The total cost per farm should thus be about $350 to $400. 
 
 Demand for Planning Services 
 
 Almost all farmers need some type of external management service 
 to help them make shortrun production decisions and longrun invest- 
 ment decisions. The demand for such services depends on the size and 
 complexity of farms, the management ability of farmers, and the fre- 
 quency with which decisions must be made. 
 
 Besides providing optimal solutions to short term production plan- 
 ning problems, the model discussed in this paper also offers insights to 
 the consequences of alternative long term investment decisions, although 
 it has not been specifically designed for this latter purpose. The produc- 
 tion planning information currently output from the system comprises: 
 (1) an enterprise budget showing what each enterprise contributes to 
 the computed profit maximum expected; (2) a plan showing the opti- 
 mum land utilization pattern for crops, including the choice of fertilizer 
 
 
Results and Conclusions 17 
 
 application rates; and (3) a plan detailing the optimal livestock opera- 
 tion, including details of buying, selling, and farrowing months and a 
 least-cost feed mix. As with any other linear programming model, 
 parametric programming and price ranging can be used to indicate the 
 effects of changing coefficients. 
 
 To justify paying a fee for decision assistance of this type, a 
 farmer requires a fairly substantial annual gross income, in excess of 
 $20,000 per year. Approximately 17 percent of all U.S. farms, produc- 
 ing over 70 percent of the agricultural products, meet this requirement 
 and are thus potential customers of a farm planning service. In Illinois, 
 the proportion of potential customers is about 40 percent, considerably 
 higher than for the nation. The farms in this class can be divided into 
 four groups. 
 
 Group 1 consists of farms grossing in excess of $60,000 per year. 
 These are large farms in terms of acreage (more than 500 acres man- 
 aged), livestock (more than 1,000 head of cattle or hogs marketed an- 
 nually), and their capital requirements (more than $1 million in fixed 
 and short term operating capital). Operators of these complex farms 
 need to supplement their own high quality managerial skill with external 
 management advisory services that can provide both short term pro- 
 duction planning advice and long term investment advice. The present 
 model would provide useful but somewhat limited results for these 
 farmers ; the lack of capital constraints in the model assumes unre- 
 stricted operating capital, a situation that is not often encountered, 
 especially on these very large farms. Many questions posed by this 
 group of farmers are long term investment decisions, which are poorly 
 handled by single-period linear programming models. Therefore, to ef- 
 fectively service very large farms, it may be necessary to develop spe- 
 cialized techniques for dealing with such questions. 
 
 Group 2 contains about five percent of Illinois farms, ranging from 
 relatively small to relatively large. The common characteristic of this 
 group is that the farms are very efficiently organized. Unlike the first 
 group, these farms are of a size that is manageable by the operator. Al- 
 though farmers in this group would be willing to pay for external 
 management assistance, a management service using a model similar 
 to ours may be of little value to them, since the farms' resources are 
 presently being used quite efficiently. They need assistance with the 
 more detailed shortrun and investment decisions. 
 
 The potential customers for a planning service that uses a model 
 similar to the one we developed will be drawn primarily from Group 3, 
 which includes perhaps 10 to 15 percent of the farms in Illinois. Again, 
 a wide variety of farm sizes are found in this group. These farms are 
 characterized by inefficient organization; the operators, though good 
 implementors who can carry out a plan correctly and on time, lack 
 managerial ability. To stay in business, these operators need external 
 
18 Results and Conclusions 
 
 sources of managerial advice, particularly detailed shortrun informa- 
 tion and investment assistance. The amount of external management 
 required depends on (1) the size and complexity of the farm; (2) the 
 basic managerial ability of the operator; and (3) the managerial abili- 
 ties of the men employed on the farm. 
 
 It is difficult, however, to convince members of this group that in- 
 creased earnings will justify the fee. Usually their financial position 
 is not very good, and our projection of $300 to $400 seems like a lot 
 to pay for such a service. Farmers who cooperated in the pilot study 
 did pay a $50 fee, but it is doubtful that they would have paid $100. 
 Nor is it likely that a commercial firm could have persuaded them to 
 pay even the $50 — most of the farmers stated that they felt they 
 were subsidizing university research when they paid the fee but were 
 willing to do so. It appears that the Group 3 farmers in the pilot study 
 would now pay a planning service's fee, but it is unlikely that those 
 not in the study would, unless influenced by an extensive educational 
 program. 
 
 The 15 to 20 percent of Illinois farmers who are comprised in Group 
 4 are poor managers and poor implementors. Farm size varies consider- 
 ably, though most tend to be relatively small (still exceeding $20,000 
 gross, however). These farmers need and might be willing to pay for 
 planning assistance with more detailed shortrun and investment de- 
 cisions, but their inability to take advantage of this assistance could 
 render it worthless. Moreover, data collection problems are usually 
 magnified many times on such farms; computer solutions based on 
 spurious data would be virtually worthless. 
 
 We have excluded almost 60 percent of Illinois farmers from the 
 above analysis. They are commercial farmers with gross sales of under 
 $20,000 and with businesses not complex enough to require compu- 
 terized management services. Most would not be willing or able to pay 
 the required fee. 
 
 Implications for the Future 
 
 A reduction in the cost of individual farm programming is neces- 
 sary before commercial application becomes feasible. The system de- 
 scribed in this report significantly decreases the direct costs of such pro- 
 gramming: total direct costs for the new system are less than half those 
 of the conventional procedure. Efforts need now to be directed towards 
 implementing procedures to reduce the costs of data collection and 
 preparation, which presently account for over 40 percent of the 
 direct costs of the new system. 
 
 Up to 20 percent (about 18,000) of the farmers in Illinois are po- 
 tential customers for a management service that will provide informa- 
 tion similar to that described here. However, before large numbers of 
 these farmers will pay for such a service, extensive training programs 
 will be necessary to show them the potential benefits. Such educational 
 
Results and Conclusions 19 
 
 programs will be the job of farm management extension personnel and 
 of those providing such services. 
 
 In addition to the planning provided by this system, there appears to 
 be a tremendous opportunity in Illinois and other Midwestern states 
 for a farm management service that could provide answers to the more 
 detailed shortrun and investment questions. Such a service would be 
 extremely valuable to farmers who are faced with decisions concerning 
 investments of tens of thousands of dollars with long term payoffs. 
 
 Commercial service organizations will need to have a well-trained 
 and diversified professional staff, the size of which will depend upon 
 how extensive the management service is. In addition, well-qualified 
 computer programmers and clerical employees will be required. 
 
 Various types of organizations such as input suppliers, buying 
 agents, financial intermediaries, farm managers, record services, and 
 universities are potential suppliers of management services. 2 The role 
 of the university as such a supplier is certainly debatable. Some argue 
 that the university should be concerned only with research and develop- 
 ment, while others argue that it should deal with more active opera- 
 tional aspects. Initially, at least, it seems that the university will have a 
 leadership role in educational efforts in the use of computerized manage- 
 ment services. 
 
 The pilot study has indicated several major structural changes in 
 the model that could improve the validity of the model and reduce the 
 cost of providing solutions. In general, these changes reduce the num- 
 ber of activities and constraints without affecting the validity of the 
 solutions. The outcome of these changes and some planned additions 
 to the model will be reported in future publications. 
 
 Some changes in the reports are also needed to make them more 
 informative and useful to farmers. Fixed costs and depreciation, for 
 example, should be included so that farmers can relate the reports to 
 accustomed budget formats. It would also be useful to have parametric 
 programming output to indicate the effects of variations in coefficients; 
 this would clarify the range of alternatives available to the farmer. 
 
 Data collection forms need to be so designed that information can 
 be collected in "farmer language" and translated by computer into the 
 form needed for input into the linear programming tableau. This will 
 greatly simplify the task of data collection by the fieldman and will 
 reduce the possibility of errors due to miscoded input data. 
 
 The results of this study indicate that a commercially viable com- 
 puterized farm planning system is feasible in the future. Exactly when 
 it will be implemented is uncertain, however, because of the educational 
 task required to make farmers aware of the potential benefits. 
 
 2 The comparative advantages of various organizations are discussed in detail 
 in C. B. Baker et al., eds., Computer- Assisted Planning Systems for Individual 
 Farms, College of Agriculture Special Publication 18, University of Illinois at 
 Urbana-Champaign, 1970. 
 
Appendix 1: The Generalized 
 Linear Programming Model 
 
 THE GENERALIZED LINEAR PROGRAMMING MODEL developed during 
 this study was designed for crop-livestock farms of the type gen- 
 erally encountered throughout the Corn Belt. In order to provide a 
 framework within which individual farm problems could be formu- 
 lated, it was necessary to provide sections for crop production, crop 
 sales, use of crops as livestock feeds, purchase of livestock feeds, and 
 livestock production. The livestock production alternatives were feeder 
 cattle, feeder hogs, and pig farrowing. No provision was made for dairy 
 or cow-calf alternatives, but these can be added in the future. Likewise, 
 no financial constraints or activities were included in the present model. 
 
 A diagram of the structure of the model is shown in Figure 2. The 
 main structural parts of the model are shown, but some additional rows 
 and columns, which handle the matrix housekeeping of cattle and swine 
 inventories and feed inventories at the beginning and end of a specific 
 planning period, have been excluded to simplify matters. 
 
 Numbered sections of the matrix contain non-zero coefficients. All 
 other parts of the matrix have zero coefficients. All sections marked 
 with the letter "A" have unitary coefficients and are entered automat- 
 ically by the matrix generator when the relevant activities are specified 
 by input parameters. All sections marked with a letter U B" have non- 
 unitary coefficients. Sections 18B and 21 B are the nutritive requirement 
 coefficients for cattle and swine feeding. Sections 16B, 17B, 19B, and 
 20B are the coefficients that give the amount of each required nutrient 
 a particular crop contributes. These sections are automatically entered 
 by the matrix generator from arrays embedded in the code. 
 
 Section 2B contains crop yield coefficients entered by the generator 
 from the individual farm data. Sections 5B, 6B, and 7B contain the 
 labor requirements for the various activities by months. These are en- 
 tered by the generator and are derived from individual farm data or 
 secondary data supplied on input cards. 1 
 
 All the restriction levels are entered into the restriction vector by 
 the matrix generator. Those labeled with the letter "C" are zeros (O's) 
 and are entered automatically. Those labeled with the letter "B" are 
 entered by the generator from the individual-farm data input on cards 
 
 1 For exact structure of the coefficients wtihin each section, see R. E. Tongate, 
 A Cost Reducing System for Applying Linear Programming Models to Planning 
 Problems of Individual Farms, Ph.D. thesis, University of Illinois at Urbana- 
 Champaign, 1969. 
 
 20 
 
Appendix 1 
 
 21 
 
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 C/) eu 
 
 Diagrammatic structure of the generalized linear programming model. The 
 size of the blocks in the figure is not intended to indicate the number of rows 
 and columns in each section. (Fig. 2) 
 
22 Appendix 1 
 
 and from noted farmer preferences. The objective function is calculated 
 from the farm data and the individual farmer's expectations and is 
 entered on cards. 
 
 Each section of the matrix is described briefly as follows: 
 
 1A — This is a section of repetitive I matrices, or matrices having 
 a diagonal of l's with O's elsewhere. The dimension of the matrices is 
 determined by the number of fields required (up to 20). The number 
 of matrices depends on the number of possible crops (up to 10) and 
 the number of technological levels within and for all crops (up to 6 in 
 one crop and 2 in each of the others). This section is potentially 20 
 rows by 480 columns. 
 
 2B — This section contains rows of crop production levels or yields 
 per acre. There is one row for each crop. The rows are arranged diag- 
 onally down through the section. This section is potentially 10 by 480. 
 
 3A — This section is a 10-element I matrix for the purpose of trans- 
 ferring crop production to storage. 
 
 4A — This section (10 X 480) is made up of a row of l's for each 
 crop, with the rows arranged diagonally through the section. This sec- 
 tion handles the acreage limitation for individual crops. 
 
 5B, 6B, and 7B — These sections contain the labor requirement co- 
 efficients for each crop and livestock type by months. Of these 32 rows, 
 the first 12 are for the crop production period; the rest allow for live- 
 stock feeding past the end of the model's arbitrary one-year period. 
 
 8A — This section (78 X 10) limits the amount of crops that can 
 be stored to the available storage capacity; it acts as a means of transfer 
 from production to storage to feed or sale. The section is made up of 
 columns of l's for each crop arranged diagonally through the matrix. 
 The first four crops can have storage accounted for by months to allow 
 for withdrawals for feed or sales by months. The remaining six crops 
 are set up on an annual storage basis. 
 
 9A, 10A, 11 A, 12A, and 13A — These sections are identical in that 
 they contain lower-left-hand triangles filled with l's. The triangles are 
 arranged diagonally through each section. This makes possible the with- 
 drawal or addition by purchase of any of four crops in storage for feed 
 to cattle or swine or for sale, all transactions being possible by months. 
 The sections are completed with rows of l's arranged diagonally for 
 annual transactions on the remaining six crops. 
 
 14A — This section contains 20 X 12 matrices repeated eight times 
 to account for each of eight possible types of cattle that can be fed. Each 
 matrix in the section contains several diagonals of l's, which account 
 for use of lot capacity by any of 12 starting months over a period of up 
 to 20 months for the model planning period. The number of diagonals 
 of l's in a matrix depends on the length of time that a particular type 
 of cattle will be on hand in the feedlot from purchase to sale. 
 
Appendix 1 23 
 
 15A — This section (29 X 96) contains a series of eight blocks of 
 matrices, one for each type of hog production (feeders and farrowing) ; 
 it contains diagonals of l's similar to those in section 14A, the number 
 of diagonals again depending upon the length of time hogs will be using 
 the facilities. 
 
 16B and 17B — These two sections (each 120 X 120) are identical; 
 they are made up of sets of diagonals, with one diagonal for each crop 
 and each nutrient required in cattle rations. The coefficients are the 
 amount of a nutrient that a specific crop contributes to the ration. Each 
 diagonal contains 12 coefficients — one for each month. 
 
 18B — This section (120 X 96) contains sets of diagonal matrices 
 that indicate the monthly nutrient requirements of each nutrient for 
 each of eight possible types of cattle. The number of diagonal rows in 
 each matrix depends on the number of months the cattle are on hand. 
 
 19B and 20B — These two sections are similar to 16B and 17B in 
 that they indicate the specific amount of the required hog nutrients con- 
 tained in each crop. Since a larger number of nutrients must be con- 
 sidered for hogs, these sections are each 136 X 120. 
 
 21B — This section, similar to 18B, contains the nutrient require- 
 ments of eight possible swine types by month and by nutrient. This 
 section is 136 X 96. 
 
 In the restriction vector, 22B gives the number of acres available 
 in each field, 24B gives the upper or lower limit allowable in acres of 
 each possible crop, 25B gives the amount of labor available for each 
 month, 26B gives the storage capacity available for each crop by month, 
 27B and 28B give the cattle and swine capacities (also by month), and 
 23C, 29C, and 30C are sets of 0's to force internal matrix transfers. 
 
Appendix 2: The Matrix Generator 
 and Report Generator 
 
 As previously explained, the purpose of the matrix-generator/ 
 report-generator system is to simplify input and solution interpre- 
 tation and thereby reduce the costs of using linear programming for 
 individual-farm planning. 
 
 The generators developed are of the "model-specific" type, with no 
 capability for handling matrix structures not previously defined in the 
 general model. In a research environment, this is somewhat inconvenient 
 because it precludes the use of the generator system to test alternate 
 model structures. The approach is, however, satisfactory for a com- 
 mercial application in which the basic model structure remains un- 
 changed for long periods. 
 
 In order to structure an individual-farm model, the matrix generator 
 requires parameters to specify what alternatives will be considered and 
 what non-unit coefficients will be entered in matrix locations. The 
 parameters and individual- farm coefficients (constraints, costs and 
 prices, labor requirements, yields) are read from cards. The secondary 
 data are extracted from arrays embedded in the matrix-generator code, 
 as are the unit coefficients. 
 
 All unit coefficients associated with a particular activity are auto- 
 matically entered into the appropriate matrix locations when a param- 
 eter specifies that activity as an alternative to be considered. For 
 example, if Crop One grown in Field One is to be considered as a 
 production alternative, l's will be generated in the Field One acreage 
 restriction rows and in the Crop One acreage restriction rows. All other 
 necessary unit coefficients are generated similarly. 
 
 The appropriate secondary data arrays are automatically entered 
 into the correct locations of the matrix when called for by a param- 
 eter string. The data generated in this manner are the various nutrient 
 levels supplied by both homegrown and purchased feeds and the vari- 
 ous nutrient requirements of livestock being fed at a particular rate. 
 These coefficients are assumed to be approximately the same from farm 
 to farm. It is assumed, for example, that every bushel of No. 2 yellow 
 corn produced anywhere in Champaign County provides the same 
 amount of digestible protein, total digestible nutrients, calcium, etc. 
 when used for feed. Or again, a 500-pound steer being fed to gain 1.5 
 pounds per day is assumed to require the same level of protein, calcium, 
 phosphorus, etc. per day regardless of the farm on which it is fed; if 
 this assumption is not acceptable, secondary data can be subclassified as 
 below average, average, and above average to reflect differences in 
 feeding efficiency due to management or some other factor. 
 
 24 
 
Appendix 2 25 
 
 Different types of individual- farm data, such as all constraint values, 
 objective function values, yields, labor requirements, etc., are input to 
 the matrix generator on different types of cards. 1 The placement of 
 values on these various card types determines where the particular 
 values will be placed in the matrix. Values in certain locations on partic- 
 ular card types require other cards to be present in the data deck. These 
 other cards are used to enter the remaining coefficients for a particular 
 activity or constraint. For example, if card 0002 specifies that corn 
 grown in Field One is to be considered as a production alternative, 
 then the matrix generator anticipates a labor requirement card, a yield 
 card, an objective function value card, a disposal activity card (whether 
 the crop is to be sold, fed, or both), an acreage restriction card, and a 
 storage restriction card. The program rejects a farm's data whenever 
 required cards are absent or illicit card codes are entered. 
 
 Card type descriptions. The card type identifiers are punched in 
 columns 1 to 5. A discussion of three card types will illustrate the man- 
 ner in which data are input into the matrix generator. 
 
 '0002' — Grown Crop Description Card. This is a mandatory card 
 since it indicates which crops are to be considered as production al- 
 ternatives. A maximum of 10 crops may be considered. 
 
 Columns 6-55 Format: 10(12, 12, II). For each crop considered as 
 grown, three values are necessarily input in the three fields provided. 
 Field No. 1: The identification number of the crop to be grown is 
 entered in this field; for example, "21" indicates that lespedeza 
 hay is to be considered as an alternative, and "01" indicates that 
 corn is to be considered. All possible crop growing activities for 
 Illinois have been assigned code numbers. 
 
 Field No. 2: The nature of the crop usage is entered here. "07" 
 indicates that the crop to be grown can be either sold or fed to live- 
 stock (both cattle and hogs). Silage, "01," can be grown and fed 
 only to cattle. Soybeans, "08," can only be grown and sold. The 
 current generalized model employs 16 such usage codes. 
 Field No. 3: This field is used to indicate if there is an acreage 
 restriction on the crop. A here indicates no acreage restriction; 1 
 means there is an acreage restriction in the amount indicated by the 
 right-hand value in the appropriate acreage restriction row. 
 
 If corn is to be considered as Crop One, columns 6 through 10 on 
 the '0002' card could be coded "01071." This would indicate that the 
 corn produced could be either sold or fed to cattle and hogs. Accord- 
 ingly, corn selling, corn fed to cattle, and corn fed to hogs activities 
 
 1 The card type is designated by the particular code found in columns 1 through 5. 
 For example, 0100's are crop labor requirement cards, 0200's are crop yield cards, 
 6000's are RHS value cards, etc. 
 
26 Appendix 2 
 
 would be generated and the appropriate unit coefficients placed in the 
 matrix. A restriction on corn acreage is also indicated (perhaps the 
 farmer plans to follow the Feed Grains Program). Similar information 
 for Crop Two is entered in columns 11 through 15, for Crop Three in 
 columns 16 through 20, and so on. 
 
 This card and the '0003' card (the Purchased Crop Description 
 Card) specify the cropping activities to be considered on a particular 
 farm. The position on these two cards (that is, the particular set of five 
 columns) identifies whether the crop is Crop One, Two, . . . , Ten and 
 whether the feed is Feed One, Two, . . . , Ten. Thereafter, the price 
 data, yield data, etc. entered for particular crops or feeds are identified 
 by crop number. 
 
 '01CCL' — Crop Growing Labor Card. This is a mandatory card for 
 each crop specified on the '0002' card. A separate card is needed for 
 each crop and for each level. 
 
 Columns 6-65 Format: 12F5.0. 'CC = ("01" through "10"). This 
 is the crop number as it appears in the matrix (Crop One, etc.). 'JJ = 
 ("0" implies "1"). This indicates the level for which the labor coeffi- 
 cients apply. The crop's monthly labor technical coefficients per acre 
 are entered here in each field. For example, on a card coded 01040, .46 
 in columns 21 through 25 indicates that Crop Four at Level One re- 
 quires .46 hours of labor per acre in April (columns 6 through 10 are 
 for January, 11 through 15 for February, etc.). 
 
 '0400' — Cattle Raising Description Cards. This card is optional 
 and is required only if cattle feeding is considered as a production 
 alternative. This card generates correct monthly nutrient requirements. 
 Columns 6-69 Format: 8(11, 12, 12, 3X). Three fields must be com- 
 pleted for each cattle type considered. A maximum of eight cattle types 
 can be considered at any one time. 
 
 Field No. 1: Expected growth rate identification (1 = 1.0 lbs. per 
 day; 2 = 1.5 lbs. per day; 3 = 1.75 lbs. per day; 4 = 2.00 lbs. per 
 day ; 5 = 2.25 lbs. per day; and 6 = 2.5 lbs. per day) . 
 Field No. 2: The starting weight identification number is entered 
 here. It is calculated as follows: 
 
 0j . -1-j Starting weight — 400 lbs. , , 
 
 Starting weight l.d. no. = —=— — ^ r- 5 rpr^ + 1 
 
 Rate of gam per 10 days 
 
 For example, animals started at 700 pounds and gaining 2.0 pounds 
 per day have a starting weight identification number of 16. 
 
 700 - 400 
 
 20 
 
 + 1 = 16 
 
 Field No. 3: The number of months for which the particular cattle 
 type is to be fed is given here. 
 
Appendix 2 27 
 
 For example, 0400 40909 indicates that type 1 cattle are expected to 
 gain two pounds per day, started at 560 pounds, and sold nine months 
 later. These three values collectively determine the appropriate monthly 
 nutrient requirements for this size animal to attain the rate of gain 
 specified. These nutrient requirements, their coefficients being drawn 
 from secondary data, are then generated in the appropriate matrix lo- 
 cations during matrix generation. 
 
 The report generator, activated by the successful solution of the 
 problem by MPS/360, accepts the MPS solution and interprets it for 
 output in a format such as that shown for the sample problem in Ap- 
 pendix 3. The report generator also computes the total receipts and 
 costs shown on the report, but its main function is to format the output. 
 
Appendix 3: An Example 
 of a Crop Production Run 
 
 FARM CHARACTERISTICS 
 
 The farm used as an example of the planning method is located on 
 gently rolling land in Champaign County, Illinois. The dominant crops 
 are corn and soybeans ; livestock enterprises consist of feeder cattle 
 and hogs, both farrowed and fed. The farm is operated by the tenant 
 and his son, both on a full-time basis. Past production records indicate 
 that the operators are above average in management ability. Their 
 planning objective is maximization of net profit within the constraints 
 of their subjective desires and existing facilities and equipment. 
 
 The available resources and the production alternatives to be con- 
 sidered are discussed in the following sections. 
 
 Land. The farm comprises 871 tillable acres divided into 10 fields. 
 The total area is rented from one landlord on a 50-50 crop-livestock 
 lease. The field acreages are shown in Table 3. 
 
 Buildings. The existing buildings are important in that they limit the 
 types and sizes of livestock and crop storage alternatives to be con- 
 sidered. The cattle feeding facilities of this farm are a barn of 160- 
 head capacity and a silo system capable of storing 700 tons of silage. 
 Farrowing facilities can accommodate 36 sows and litters (averaging 
 8.5 pigs per litter) simultaneously, and the hog finishing facilities can 
 accommodate 600 head. Total on- farm grain storage capacity is 62,000 
 bushels, all of which is used for corn. In the past any beans grown 
 have been stored in town. 
 
 Labor. The labor of the two operators is to be supplemented by 
 a full-time hired man in early 1971. Therefore, three full-time 
 equivalents will be available except during vacations, taken during slack 
 periods. The manhours of available labor during the period covered by 
 the crop production plan are shown in Table 4. 
 
 The 32 months of labor are shown to accommodate the 12 months 
 (October 1969 to September 1970) of the crop production period, the 
 
 Table 3. — Field Acreages 
 
 Field 
 
 Acreage 
 
 Field 
 
 Acreage 
 
 1 
 
 121 
 
 6 
 
 70 
 
 2 
 
 50 
 
 7 
 
 112 
 
 3 
 
 101 
 
 8 
 
 112 
 
 4 
 
 51 
 
 9 
 
 105 
 
 5 
 
 119 
 
 10 
 
 30 
 
 28 
 
 

 
 Appendix 
 
 3 
 
 
 29 
 
 
 Table 4. — Labor Avail 
 
 f ab/e per 
 
 Month 
 
 
 Month 
 
 Man- 
 
 Month 
 
 Man- 
 
 Month 
 
 Man- 
 hours 
 
 
 hours 
 
 
 hours 
 
 
 October 1969 
 
 475 
 
 August 1970 
 
 587 
 
 June 1971 
 
 792 
 
 November 1969 
 
 462 
 
 September 1970 
 
 537 
 
 July 1971 
 
 792 
 
 December 1969 
 
 384 
 
 October 1970 
 
 648 
 
 August 1971 
 
 792 
 
 January 1970 
 
 384 
 
 November 1970 
 
 648 
 
 September 1971 
 
 720 
 
 February 1970 
 
 386 
 
 December 1970 
 
 576 
 
 October 1971 
 
 648 
 
 March 1970 
 
 455 
 
 January 1971 
 
 576 
 
 November 1971 
 
 648 
 
 April 1970 
 
 531 
 
 February 1971 
 
 576 
 
 December 1971 
 
 576 
 
 May 1970 
 
 604 
 
 March 1971 
 
 648 
 
 January 1972 
 
 576 
 
 June 1970 
 
 606 
 
 April 1971 
 
 720 
 
 February 1972 
 
 576 
 
 July 1970 
 
 589 
 
 May 1971 
 
 792 
 
 March 1972 
 April 1972 
 May 1972 
 
 648 
 720 
 792 
 
 12 months during which these crops are disposed of (October 1970 to 
 September 1971), and an additional eight months to allow feeder live- 
 stock to be introduced during the later part of the disposal period. 
 This long extra period of time must be included to account for all live- 
 stock alternatives, but any plans for longer than 12 months are neces- 
 sarily tentative and are updated at subsequent runs. 
 
 Capital. Shortrun operating capital is not an effectively limiting 
 resource on this farm. The owner has alternative sources of operating 
 capital at the going interest rate. There are definitely long term capital 
 limitations, but since we are concerned only with the immediate pro- 
 duction period, these limitations can safely be ignored. 
 
 Machinery. Enough equipment is available to operate the farm 
 under any feasible cropping system. Thus, machinery is not a limiting 
 resource for the crop and livestock alternatives under consideration. 
 Table 5 gives a summary of the physical constraints for the farm. 
 The objective is to select the combination of activities that will maxi- 
 mize the return from these limited resources over the coming production 
 period. The next step is therefore to determine which alternative activi- 
 ties are to be considered. The operator is consulted here so that only 
 enterprises he will consider are involved. As a start, his present plan 
 and his past records are reviewed. 
 
 Crop alternatives. The farm has been planted primarily in corn, for 
 grain and silage, and in soybeans, with a small acreage of wheat. These 
 crops are the enterprises to be considered as production alternatives 
 in this crop production run. 
 
 Livestock alternatives. In each of the three years, the operator has 
 fed 100 to 200 head of cattle and sold up to 1,200 hogs. Some of the 
 hogs sold are farrowed on the farm. Feeder cattle, feeder pigs, and hog 
 farrowing are therefore the admissible livestock alternatives. 
 
30 Appendix 3 
 
 Table 5. — Names of Production Constraints 
 
 Acres in fields 1 to 10 
 
 Labor available in months 1 to 32 
 
 Storage capacity for corn in months 13 to 24 
 
 Storage capacity for silage in months 13 to 24 
 
 Cattle f eedlot capacity in months 13 to 24 
 
 Swine farrowing capacity in months 13 to 24 
 
 Swine finishing capacity in months 13 to 24 
 
 D.M. requirements for cattle in months 13 to 24 
 
 T.D.N, requirements for cattle in months 13 to 24 
 
 D.P. requirements for cattle in months 13 to 24 
 
 Ca requirements for cattle in months 13 to 24 
 
 P requirements for cattle in months 13 to 24 
 
 Urea requirements for cattle in months 13 to 24 
 
 Crude fiber requirements for swine in months 13 to 24 
 
 T.D.N, requirements for swine in months 13 to 24 
 
 Crude protein requirements for swine in months 13 to 24 
 
 Ca requirements for swine in months 13 to 24 
 
 P requirements for swine in months 13 to 24 
 
 Lysine requirements for swine in months 13 to 24 
 
 Methionine requirements for swine in months 13 to 24 
 
 Tryptophan requirements for swine in months 13 to 24 
 
 After determining the possible crop and livestock production al- 
 ternatives, numerous other activity choices are implied: What levels of 
 crops and types of livestock should be considered, 1 in which fields can 
 various crops be grown, in what months can these crops be sold, what 
 livestock feeds are to be considered, and in what months can these feeds 
 be purchased ? The alternative activities for the farm in this example are 
 summarized in Table 6. 
 
 MODEL SPECIFICATIONS 
 
 The matrix coefficients used to specify the matrix for the example 
 are discussed in the sections below. 
 
 Objective function values. The expected variable production costs 
 per acre for each of the five crops considered were calculated using 
 past data from the farm, with secondary data derived from cost sur- 
 veys used as a guide. Corn and corn silage were considered at two 
 levels of fertilization, while soybeans and wheat were considered at one 
 level. The variable costs used in the problem are shown in Table 7. 
 
 A 5-year monthly average selling price for corn, soybeans, and 
 wheat was calculated from records made available by the local elevator ; 
 these averages gave the expected seasonal price variation. Using Sep- 
 
 1 Production levels are defined here to be such variables as rates of fertilizer 
 application, plant population, row spacing, etc., which affect the yield or the 
 growing cost of the particular crop. Types are defined here to be such variables 
 as rates of gain, buying and selling weight, length of feeding period, etc., which 
 affect the objective function value. 
 
Appendix 3 31 
 
 Table 6. — Production Alternatives 
 
 Corn at fertilizer level 1 (200-100-100) in fields 1 to 10 
 
 Corn at fertilizer level 2 (160-80-80) in fields 1 to 10 
 
 Soybeans (no fertilizer) in fields 1 to 10 
 
 Wheat (80-40-40) in fields 1 to 10 
 
 Corn silage level 1 (200-100-100) in fields 1 to 10 
 
 Corn silage level 2 (160-80-80) in fields 1 to 10 
 
 Feed grown corn to cattle in months 13 to 24 
 
 Feed grown corn to swine in months 13 to 24 
 
 Feed bought alfalfa hay to cattle in months 13 to 24 
 
 Feed bought mixed hay to cattle in months 13 to 24 
 
 Feed grown silage to cattle in months 13 to 24 
 
 Feed bought protein supplement to cattle in months 13 to 24 
 
 Feed bought oats to cattle in months 13 to 24 
 
 Feed bought oats to swine in months 13 to 24 
 
 Feed bought protein supplement to swine in months 13 to 24 
 
 Feed bought dical to swine in months 13 to 24 
 
 Feed bought lime to swine in months 13 to 24 
 
 Sell corn in months 13 to 24 
 
 Sell beans in months 13 to 24 
 
 Sell wheat in months 13 to 24 
 
 Start feeding 560 lb. steers for 9 months, at 2.00 lbs. per day, in months. ... 13 to 24 
 Start feeding 760 lb. steers for 7 months, at 2.00 lbs. per day, in months. ... 13 to 24 
 
 Farrow 1 litter pigs to be sold 5 months later, in months 13 to 24 
 
 Start feeding 40 lb. feeder pigs for 4 months at 1.5 lbs. per day, in months. . . 13 to 24 
 Dummv feeding activities for months 25 to 32 
 
 Table 7. — Expected Variable Production Costs for Crops in Dollars 
 
 Corn level 1 (200-100-100) 53.25 
 
 Corn level 2 (160-80-80) 48.45 
 
 Beans 31.85 
 
 Wheat 24.12 
 
 Silage level 1 (200-100-100) 61.20 
 
 Silage level 2 (160-80-80) 56.40 
 
 tember, 1969, prices as a base and the monthly futures prices, these 5- 
 year monthly averages were adjusted to arrive at the expected monthly 
 selling prices for corn, soybeans, and wheat (Table 8). Xo selling prices 
 were calculated for corn silage since the corn would be harvested as 
 grain rather than as silage if it were unprofitable to feed silage. Storage 
 costs were then deducted from the expected monthly selling prices and 
 the net prices were the ones actually used for each crop. 
 
 Expected monthly purchase prices for the various feeds (Table 9) 
 were also estimated by using local elevator 1969 feed prices and the 
 selling prices previously determined (for feeds also grown). 
 
 Objective function values for all livestock activities were estimated 
 using the futures market, the selling prices in Chicago for the past five 
 years, and detailed selling prices and purchase costs from the individual 
 farm's 1969 records. (These prices were all for the relevant grades being 
 considered on the farm.) Using the September, 1969, buying and selling 
 
32 
 
 Appendix 3 
 
 Table 8. 
 
 — Expected Monthly Selling Prices in Dollars Per Bushel 
 
 Month 
 
 Corn Wheat Soybeans 
 
 October 1.06 
 
 November 1.07 
 
 December 1 . 10 
 
 January 1.11 
 
 February 1 . 13 
 
 March 1.15 
 
 April 1.16 
 
 May 1.18 
 
 June 1.17 
 
 July 1.15 
 
 August 1.13 
 
 September 1 . 09 
 
 1.20 
 
 2.25 
 
 1.22 
 
 2.26 
 
 1.23 
 
 2.28 
 
 1.24 
 
 2.31 
 
 1.25 
 
 2.33 
 
 1.26 
 
 2.35 
 
 1.28 
 
 2.37 
 
 1.30 
 
 2.39 
 
 1.27 
 
 2.40 
 
 1.24 
 
 2.39 
 
 1.18 
 
 2.38 
 
 1.19 
 
 2.34 
 
 Table 9. — Expected Monthly Feed Purchase Prices in Dollars 
 
 Month 
 
 Corn 
 
 Alfalfa 
 hay 
 
 Oats 
 
 Protein 
 42% 
 hog 
 
 supple- 
 ment 
 
 Mixed 
 hay 
 
 Lime 
 
 Dical 
 
 Protein 
 40% 
 cattle 
 supple- 
 ment 
 
 
 (bu.) 
 
 (cwt.) 
 
 (bu.) 
 
 (cwt.) 
 
 (cwt.) 
 
 (cwt.) 
 
 (cwt.) 
 
 (cwt.) 
 
 October 
 
 1.09 
 
 1.40 
 
 .67 
 
 6.90 
 
 1.15 
 
 2.10 
 
 6.90 
 
 5.80 
 
 November 
 
 1.11 
 
 1.45 
 
 .68 
 
 6.90 
 
 1.17 
 
 2.10 
 
 6.90 
 
 5.80 
 
 December 
 
 1.13 
 
 1.47 
 
 .69 
 
 6.90 
 
 1.18 
 
 2.10 
 
 6.90 
 
 5.80 
 
 January 
 
 1.15 
 
 1.49 
 
 .72 
 
 6.90 
 
 1.20 
 
 2.10 
 
 6.90 
 
 5.80 
 
 February 
 
 1.17 
 
 1.51 
 
 .75 
 
 6.90 
 
 1.21 
 
 2.10 
 
 6.90 
 
 5.80 
 
 March 
 
 1.19 
 
 1.53 
 
 .77 
 
 6.90 
 
 1.22 
 
 2.10 
 
 6.90 
 
 5.80 
 
 April 
 
 1.21 
 
 1.56 
 
 .76 
 
 6.90 
 
 1.24 
 
 2.10 
 
 6.90 
 
 5.80 
 
 May 
 
 1.23 
 
 1.49 
 
 .75 
 
 6.90 
 
 1.27 
 
 2.10 
 
 6.90 
 
 5.80 
 
 June 
 
 1.24 
 
 1.46 
 
 .71 
 
 6.90 
 
 1.19 
 
 2.10 
 
 6.90 
 
 5.80 
 
 July 
 
 1.22 
 
 1.43 
 
 .68 
 
 6.90 
 
 1.13 
 
 2.10 
 
 6.90 
 
 5.80 
 
 August 
 
 1.18 
 
 1.41 
 
 .69 
 
 6.90 
 
 1.15 
 
 2.10 
 
 6.90 
 
 5.80 
 
 September 
 
 1.12 
 
 1.38 
 
 .70 
 
 6.90 
 
 1.17 
 
 2.10 
 
 6.90 
 
 5.80 
 
 prices as base prices, and using the futures prices, the 5-year monthly 
 price averages were adjusted to arrive at the expected buying and sell- 
 ing prices (Tables 10 and 11). Total purchase cost and variable produc- 
 tion expenses, except labor and feed (Table 12), were deducted from 
 the total sales value to obtain the objective function coefficient for each 
 type in each month. 
 
 The objective function values for farrowing were calculated by 
 deducting variable production costs per litter, except feed and labor, 
 from the expected sales value per litter. An average of 8.5 pigs per 
 litter was assumed to be sold from each litter farrowed. Thus, the sales 
 value per litter is 8.5 times the expected selling value. 
 
 Technical coefficients. Monthly labor requirements for enterprises 
 were not available from the farm's records. Therefore, these coefficients 
 
Appendix 3 
 
 33 
 
 Table 10. — Expected Cattle Buying and Selling Prices 
 (Dollars Per 100 Lbs.) 
 
 Type I: 
 
 Steers 1 
 
 Dought at 560 lbs. 
 
 Type II 
 
 : Steers 
 
 bought at 760 lbs. 
 
 and sold 9 mon 
 
 ths later at 1,100 
 
 and sold 7 mon 
 
 iths later at 1,180 
 
 lbs. — 
 
 2.0 lbs. 
 
 daily rate of gain 
 
 lbs. — 
 
 2.0 lbs. 
 
 daily rate of gain 
 
 Purchase 
 
 Pur- 
 chase 
 price 
 
 Selling Selling 
 
 Purchase 
 
 Pur- 
 chase 
 price 
 
 Selling Selling 
 
 month 
 
 month price 
 
 month 
 
 month price 
 
 October 
 
 33.00 
 
 July 27.79 
 
 October 
 
 33.00 
 
 April 27.75 
 
 November 
 
 32.00 
 
 August 28.18 
 
 November 
 
 32.00 
 
 May 27.30 
 
 December 
 
 31.00 
 
 September 28.33 
 
 December 
 
 31.00 
 
 June 27.40 
 
 January 
 
 30.00 
 
 October 29.00 
 
 January 
 
 30.00 
 
 July 27.79 
 
 February 
 
 30.25 
 
 November 28.50 
 
 February 
 
 30.25 
 
 August 28.18 
 
 March 
 
 30.70 
 
 December 27.75 
 
 March 
 
 30.70 
 
 September 28.33 
 
 April 
 
 30.15 
 
 January 27.00 
 
 April 
 
 30.15 
 
 October 29 . 00 
 
 May 
 
 30.80 
 
 February 27.20 
 
 May 
 
 30.80 
 
 November 28.50 
 
 June 
 
 30.85 
 
 March 27.66 
 
 June 
 
 30.85 
 
 December 27.75 
 
 July 
 
 31.00 
 
 April 27.66 
 
 July 
 
 31.00 
 
 January 27.00 
 
 August 
 
 31.40 
 
 May 27.64 
 
 August 
 
 31.40 
 
 February 27.20 
 
 September 
 
 31.50 
 
 June 27.68 
 
 September 
 
 • 31.50 
 
 March 27.66 
 
 Table 77. — Expected Hog Buying and Selling Prices 
 (Dollars Per 700 Lbs.) 
 
 Purchase 
 
 Pur- 
 chase 
 price 
 
 Selling 
 
 Selling 
 
 Farrowing 
 
 Selling 
 
 Selling 
 
 month 
 
 month 
 
 price 
 
 month 
 
 month 
 
 price 
 
 October 
 
 21.40 
 
 February 
 
 20.10 
 
 October 
 
 March 
 
 20.40 
 
 November 
 
 21.55 
 
 March 
 
 20.40 
 
 November 
 
 April 
 
 21.80 
 
 December 
 
 21.90 
 
 April 
 
 21.80 
 
 December 
 
 May 
 
 22.10 
 
 January 
 
 22.30 
 
 May 
 
 22.10 
 
 January 
 
 June 
 
 22.60 
 
 February 
 
 22.65 
 
 June 
 
 22.60 
 
 Februarv 
 
 July 
 
 22.85 
 
 March 
 
 23.00 
 
 July 
 
 22.85 
 
 March 
 
 August 
 
 22.10 
 
 April 
 
 22.80 
 
 August 
 
 22.10 
 
 April 
 
 September 
 
 21.60 
 
 May 
 
 22.40 
 
 September 
 
 21.60 
 
 May 
 
 October 
 
 21.00 
 
 June 
 
 21.70 
 
 October 
 
 21.00 
 
 June 
 
 November 
 
 20.85 
 
 July 
 
 21.40 
 
 November 
 
 20.85 
 
 July 
 
 December 
 
 20.40 
 
 August 
 
 20.90 
 
 December 
 
 20.40 
 
 August 
 
 January 
 
 20.00 
 
 September 
 
 20.30 
 
 January 
 
 20.00 
 
 September 
 
 February 
 
 22.20 
 
 Table 12. — Expected Non-Labor, Non-Feed, Variable 
 Production Costs for Livestock (in Dollars) 
 
 Type 
 
 Expected production cost 
 
 Type I cattle (per head) 5 . 44 
 
 Type II cattle (per head) 5 .44 
 
 Farrowing (per litter) 26 . 96 
 
 Feeder hogs (per head) 4.86 
 
34 
 
 Appendix 3 
 
 Table 13. — Expected Crop Labor Requirements Per Acre 
 and Per Month (Man-hours) 
 
 Month 
 
 Corn Soybeans Wheat 
 
 Silage 
 
 October. . . 
 November. 
 December. 
 January. . . 
 February. . 
 
 March 
 
 April 
 
 May 
 
 June 
 
 July 
 
 August . . . 
 September 
 October. . . 
 November. 
 December. 
 
 57 
 
 14 
 
 07 
 
 
 14 
 
 32 
 
 33 
 
 15 
 
 32 
 
 52 
 
 46 
 
 10 
 
 52 
 
 36 
 
 69 
 
 25 
 
 36 
 
 .28 
 
 62 
 
 56 
 
 28 
 
 17 
 
 13 
 
 15 1 
 
 40 
 
 26 
 
 65 
 
 6 
 
 75 
 
 76 
 
 20 
 
 
 14 
 
 40 
 
 
 
 
 Table 14. — Livestock Labor Requirements Per Head Per Month (Man-hours)* 
 
 Tvpe I Tvpe II *- Feeder 
 
 Month cattle cattle F^™* hogs 
 
 (per head) (per head) lper lltter; (per head) 
 
 Month 1 23 .23 3.5 .26 
 
 Month 2 36 .36 2.1 .26 
 
 Month 3 42 .42 2.1 .26 
 
 Month4 42 .42 2.1 .26 
 
 Month 5 38 .38 2.1 
 
 Month 6 43 .43 2.1 
 
 Month 7 39 .39 
 
 Month 8 38 .38 
 
 Month 9 36 .36 
 
 Month 10 53 .53 
 
 Month 11 55 .55 
 
 Month 12 38 .38 
 
 a Month 1, for cattle, is October; month 1, for farrowing, is the month in which farrowing 
 takes place. The requirements for feeder hogs are the same in each month. 
 
 were estimated using secondary data derived from labor use surveys. 
 For each crop, data were available by month according to equipment 
 size. Tractor horsepower and equipment sizes were recorded during 
 the farm interview to determine correct labor coefficients (Table 13). 
 
 Monthly labor coefficients for livestock (Table 14) were also de- 
 termined from secondary data. These secondary coefficients were avail- 
 able according to feeding setup (pasture versus confinement, slotted 
 floors versus solid floors, etc.) and degree of feeding automation, de- 
 termined during the interview. 
 
 The monthly cattle labor coefficients were determined primarily by 
 seasonal conditions regardless of the starting month. For example, the 
 per head labor requirement for October would be the same for a partial- 
 
 
Appendix 3 
 
 35 
 
 Field 
 number 
 
 Table 15. — Expected Crop Yields Per Acre by Field 
 
 Corn 
 (level 1) 
 
 Corn 
 (level 2) 
 
 Soy- 
 beans 
 
 Wheat 
 
 Corn 
 
 silage 
 
 (level 1) 
 
 Corn 
 
 silage 
 
 (level 2) 
 
 bu. 
 
 1 140 
 
 2 132 
 
 3 129 
 
 4 130 
 
 5 136 
 
 6 126 
 
 7 124 
 
 8 123 
 
 9 120 
 
 10 141 
 
 bu. 
 
 bu. 
 
 bu. 
 
 cwt. 
 
 cwt. 
 
 135 
 
 34 
 
 59 
 
 395 
 
 380 
 
 128 
 
 33 
 
 57 
 
 370 
 
 360 
 
 125 
 
 32.5 
 
 58 
 
 362 
 
 350 
 
 126 
 
 29 
 
 51 
 
 365 
 
 353 
 
 130 
 
 30.5 
 
 49 
 
 373 
 
 365 
 
 121 
 
 27 
 
 46 
 
 340 
 
 332 
 
 118 
 
 25 
 
 44 
 
 332 
 
 324 
 
 119 
 
 28.5 
 
 41 
 
 336 
 
 326 
 
 116 
 
 27 
 
 41 
 
 329 
 
 320 
 
 136 
 
 34 
 
 58 
 
 396 
 
 382 
 
 lar animal whether that is the first, fourth, or ninth month the animal 
 has been on feed. The swine labor coefficients, on the other hand, were 
 assumed to be the same in the starting month regardless of the particu- 
 lar month. The same is true for months two through six for farrowing. 
 
 The expected yields derived for the various crops in each of the 
 fields (Table 15) were based on past records for the farm. On this 
 particular farm, field maps showing fertilizer applications and crop 
 yields were available for each field for each of the last three years. 
 
 The nutrient provisions of various grown and purchased feeds and 
 the various monthly nutrient requirements for livestock were estimated 
 entirely from secondary data. 2 Individual farm data are not available 
 for these coefficients. 
 
 These represent all the data necessary to program this particular 
 farm using the relevant subset of the general model. 
 
 RESULTS 
 
 Report No. I (see pages 38-39) 
 
 Report No. I, the production plan, contains physical information 
 specific to each enterprise. The production plan is composed of four 
 sections: (1) crop production; (2) cattle production; (3) swine pro- 
 duction ; and (4) livestock feeding plan. 
 
 Section I — crop production. In the first part of this section the 
 total acreage, average yield, and total production are given for each 
 
 2 See, for example, G. P. Lofgreen, "Digestible Protein, Total Digestible Nutrients, 
 and Net Energy Requirements for Maintenance and Gain of Beef Cattle," Uni- 
 versity of California Department of Animal Science ; Frank Morrison, Feeds and 
 Feeding, Morrison Publishing Company, Clinton, Iowa, 22nd ed., 1959; and D. E. 
 Becker, A. H. Jensen, and B. G. Harmon, "Balancing Swine Rations," University 
 of Illinois College of Agriculture, Circular 866. 
 
36 Appendix 3 
 
 crop. The second part of this section provides a production recommen- 
 dation by enterprise and field. In addition, the technological (fertilizer) 
 level, the expected yield, the acres in each field to be utilized by a par- 
 ticular crop, and the expected variable growing cost are indicated. For 
 example, line 7 indicates that 86 acres of corn at Level One (200-100- 
 100; lbs. N-P-K) should be grown in Field One with an expected yield 
 of 140 bushels per acre. The expected variable production costs for 
 Field One are $53.25 per acre. 
 
 Section II — cattle production. This section provides information 
 on each lot of feeder cattle that is recommended for purchase. The 
 description of each lot is, in order, buying weight, length of feeding 
 period, final weight, optimal rate of gain per day, month bought and 
 sold, number of head, pounds of beef produced, return per head, pur- 
 chase price, and sale price per 100 pounds. All purchases are recorded 
 in this section whether the feeders are to be sold during the immediate 
 12-month period or are to be in ending inventory at the end of this 
 period. The pounds produced during the 12-month period for each lot 
 is recorded for all animals. The values given in the expected return 
 column are the respective objective function values. These values, for 
 example $128.00 in line 19, are calculated by deducting the purchase 
 price and variable production expenses from the selling price per head. 
 
 Section III — swine production. A specific description of each lot 
 of pigs farrowed or fed, if called for in the optimal solution, is given 
 here. These data include length of feeding period, expected average 
 litter size, purchase weight for feeders, selling weight, month farrowed, 
 number of litters farrowed, pounds produced, expected return, and pur- 
 chase and sale prices. This information is interpreted as in the cattle 
 section. In this specific case, only feeder pigs are recommended. 
 
 Section IV — livestock feed plan. This section provides a monthly 
 feeding plan for both cattle and hogs. For purchased feeds, the ex- 
 pected monthly purchase price and the quantity to be purchased (num- 
 ber of bushels or hundredweights) are given. For grown feeds only the 
 quantity to be fed is given. 
 
 Report No. II (see page 40) 
 
 Report No. II, the budget, contains a financial summary of expected 
 receipts and expenses for the planning period. It is composed of three 
 sections: (1) receipts and expenses for crops; (2) receipts and ex- 
 penses for cattle; and (3) receipts and expenses for swine. 
 
 Section I — crop receipts and expenses. Each crop sale is listed sepa- 
 rately, giving the crop name, the selling month, the selling price, the 
 number of units sold, and the total receipts of each sale. There may be 
 more than one sale listed for each crop, as there is for corn in this 
 example. On this farm, more corn is planned for production than can 
 
Appendix 3 37 
 
 be stored on the farm. Therefore, the production in excess of storage 
 capacity is sold at harvest at $1.06. The remainder is fed to livestock or 
 sold in' May at $1.18. The total value of crops sold ($112,292) is the 
 summation of all crop sales. In order to get an accurate valuation for 
 crops grown, crops fed must be valued at the price at which they could 
 be sold. Thus, the value placed on crops fed is the expected selling price 
 in the respective feeding month, not the growing cost. The summation 
 of the crop sales and crops fed accounts is the total crop value. Variable 
 production expenses for all crops are deducted from the total crop value 
 to get the expected return above direct cost for grain ($76,171). 
 
 Section II — cattle receipts and expenses. Each cattle sale, during 
 the 12-month period being programmed, is recorded by type. This in- 
 cludes all animals in inventory at the start of the period and all lots 
 bought and sold during the period. Lots that are purchased but not sold 
 during the period are not entered on this report. (They are recorded on 
 Report No. I, however.) For example, line 16 indicates that 160 steers 
 weighing 560 pounds are bought, fed for nine months, and sold at ap- 
 proximately 1,100 pounds. The optimal daily rate of gain was deter- 
 mined to be two pounds. The objective function value per head times 
 160 gives the sales value of $20,480. The total cattle feed expense 
 (grown and purchased) is deducted from the total sales figures to ar- 
 rive at the expected return above direct production costs for cattle 
 ($11,297). 
 
 Section III — swine receipts and expenses. Receipts and expenses 
 in this section are calculated like those for cattle and are interpreted in 
 the same way. Following the swine section, an expected return 
 above direct production cost for the entire farm ($104,389) is calcu- 
 lated by summing the return figures of Sections I through III. 
 
 SUMMARY 
 
 The reports presented as an example are imperfect in several areas. 
 First, the format is not entirely satisfactory and needs to be consider- 
 ably altered to make the reports useful for real-world users. Second, 
 the values shown in the reports are subject to roundoff errors ; hence, 
 there appear to be disagreements between some of the computed num- 
 bers (which are, however, accurate). Third, the "expected net profit" 
 is computed as the return above variable costs and is not comparable 
 with the usual definition of net profit, which takes into account fixed 
 costs and depreciation. Fourth, the "inventory change" entry on Report 
 II shows a zero value because this facility has not yet been activated. 
 
 Despite its present shortcomings, however, the system discussed in 
 this report shows great promise and may lead to a system usable in 
 commercial applications of farm planning. In addition, the matrix- 
 generator/report-generator technique may facilitate the use of linear 
 programming in research in agricultural economics. 
 
38 
 
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