• TABLE OF CONTENTS
HIDE
 Front Cover
 Abstract
 Table of Contents
 Introduction
 Analysis
 Results
 Summary
 Limitations
 Need for further research
 Reference














Group Title: University of Florida. Agricultural Experiment Stations. Economics Report ; 102
Title: An optimal farm enterprise organization in north and west Florida
CITATION THUMBNAILS PAGE IMAGE ZOOMABLE
Full Citation
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Permanent Link: http://ufdc.ufl.edu/UF00027399/00001
 Material Information
Title: An optimal farm enterprise organization in north and west Florida
Series Title: Economics report
Physical Description: iii, 36 p. : map ; 28 cm.
Language: English
Creator: Prevatt, J. Walter
Publisher: Food and Resource Economics Dept., Agricultural Experiment Stations, Institute of Food and Agricultural Sciences, University of Florida
Place of Publication: Gainesville Fla
Publication Date: 1981
 Subjects
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Bibliography: Bibliography: p. 36.
Statement of Responsibility: J. Walter Prevatt, John E. Reynolds, Bryan E. Melton.
General Note: Cover title.
 Record Information
Bibliographic ID: UF00027399
Volume ID: VID00001
Source Institution: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: aleph - 002199020
oclc - 07520264
notis - ALD8900

Table of Contents
    Front Cover
        Front Cover
    Abstract
        Page i
    Table of Contents
        Page ii
        Page iii
    Introduction
        Page 1
        Page 2
    Analysis
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
    Results
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
    Summary
        Page 32
    Limitations
        Page 33
    Need for further research
        Page 34
        Page 35
    Reference
        Page 36
Full Text
April
K 0'`
^ :.


1981


Economics Report 102


An Optimal Farm Enterprise
Organization in
North and West Florida


HUME LIBRARY
APR 1 1981
I.F.A.S. Unv. of Flot ida


Food and Resource Economics Department
Agricultural Experiment Stations
Institute of Food and Agricultural Sciences
University of Florida, Gainesville 32611


J. Walter Prevatt


John E.


Reynolds


Bryan E. Melton


I _










ABSTRACT


A profit maximizing dynamic linear programming model was developed to
determine the optimal levels of field crop, forage and beef cattle enter-
prises. Constraints in the model were placed on (1) land, (2) labor, (3)
operating capital, (4) tobacco and peanut allotments, (5) farm manager,
(6) dry matter, (7) metabolizable energy and (8) digestible protein. The
programming model was used to develop the optimal organization of farm
resources given prices over a five-year planning horizon, 1973-77.

The profit maximizing solution included producing a combination of
field crops, forages and beef cattle enterprises. These activities pro-
duced an average annual profit of $29,655.50 over the five-year planning
horizon. Profit ranged from $12,190 in 1976 when all yearling heifers
were retained and both field crop and beef cattle prices were low to a
high of $71,342 in 1974 when field crop prices were high and many beef
cattle were liquidated.

Key words: Field crops, forages, beef cattle, profit, resources,
constraints and dynamic linear programming.











TABLE OF CONTENTS


ABSTRACT. . . . .

INTRODUCTION. . . . .

ANALYSIS. . . . .

FIRM THEORY. . . .

PROGRAMMING MODEL. . . .

CODING . . . .

OBJECTIVE FUNCTION . . .

RESTRICTIVE CONSTRAINTS OF THE MODEL

ACTIVITIES OF THE MODEL. . .

Field Crops. . . .
Forages . . .
Beef Cattle. . . .
Miscellaneous Activities .

RESULTS . . . . .

SUMMARY . . . . .

Limitations . . .


Need for Further Research. .

REFERENCES . . . .


Page
i

1

3

3

4

6

8

8

12

12
12
17
18

18

32

33
34

36


. . . .

. . .. ..










LIST OF TABLES

Table Page
1 Code abbreviation, description, constraint and unit 9
of measurement for row elements of the jth year in
the dynamic linear programming model . ..

2 Code abbreviation, description and unit of measure- 13
ment from column activities for one submatrix (one
year) of the dynamic linear programming model). ..

3 Optimal activity levels for field crops and forages 19
during the five-year planning horizon . . .

4 Beef cattle inventories immediately prior to culling 20
(October sales) in each year. . . . .

5 Input costs and output revenues for optimal field 24
crop activities for each of the five years. .

6 Input costs and optimal forage activities for each 25
of the five years . . . . .

7 Beef cattle sold in each year by age. . .. .. 27

8 Input costs and output revenues for optimal beef 29
cattle activities for each of the five years. . .

9 Profit and loss statements for each year of the 30
planning horizon . . . . .


LIST OF FIGURES
Figure Page

1 Planning Districts, I, II, and III in North and 2
West Florida . . . . .

*2 Organization of multiperiod programming activity 7
matrix . . . . . .










INTRODUCTION


Agriculture in North and West Florida (Planning Districts I, II, and

III in Figure 1) is important for many reasons. The direct contribution

of agriculture to income and employment is relatively small, but it's

indirect contribution through support industries and manufacturing is

quite large [7]. The production of agricultural commodities in this area

represents an important segment of Florida's agriculture. In 1975, the

area's farm income from cash receipts and other income totaled $413

million or approximately 16 percent of the state's farm income from cash

receipts and other income [8].

Traditionally, agriculture in North and West Florida has been domin-

ated by field crops and beef cattle enterprises. The area is not a major

beef cattle producing area. However, beef cattle production when coupled

with field crops may profitably utilize the available resources in the

following ways: (1) land that is not suitable for field crop production

may be used for pasture production, (2) available labor may be used more

uniformly throughout the year and (3) machinery and equipment may be used

more economically.

The major objective of this study was to develop a profit-maximizing

model to determine the optimal farm resource organization. The determi-

nation of the optimal enterprise organization for given resource situa-

tions will provide information for production planning at the firm level.






Other income is comprised of government payments, imputed income and
rent received.

































































Figure 1. Planning Districts I, II, and III in North and West Florida.


j/ ^ ^










ANALYSIS


A firm level approach was taken to determine the optimal farm resource

organization [51. The analysis assumed a general applicability of produc-

tion practices most common among North and West Florida producers. Recom-

mended production practices for each of the potentlnl field crops, forages

and beef cattle enterprises were specified for the development of the

budgets. The data for the budgets were assembled with the help of cooper-

ating agribusinessmen, extension specialist and area economists [6].

A dynamic linear programming model which maximized profit from the

production of field crops, forages and beef cattle enterprises over a

five-year planning horizon (1973-77) was used to analyze the data. Con-

straints on land, labor and capital were incorporated into the model.

The quantity of land used for cropland, pasture and range were each

restricted to 166.0 acres per year. A full-time farm manager was required

to provide labor and management for the production processes. The avail-

ability of the manager's labor was constrained by months and totaled

2,792 hours annually. Operating capital was constrained to a maximum of

$100,000 per year. Flue-cured tobacco and peanut allotments were con-

strained to 5.0 and 15.0 acres, respectively.

A Brahman-cross beef cattle herd was used in this analysis as a

representative herd for North Florida. Monthly nutritional requirements

were obtained to account for physical and biological changes during the

annual production of beef cattle activities [4].


Firm Theory

The theory of the firm entails the determination of the optimal









combination of variable factors for a given product and the optimal com-

bination of different products for maximizing profit from a specific set

of resources [2]. The producer is psuglly able to vary the levels of both

factors and products which allows him to change production with price

variability. The appropriate functions necessary to determine the optimal

levels are the production and cost functions [2]. These functions are

used to achieve the optimal level of production that will maximize profit.


Programming Model

The organization problem in this study is formulated as a standard

linear programming problem in which production periods are linked and a

single objective function is maximized. As an extension of linear program-

ming, Loftsgard and Heady [3] proposed a model that would optimize over

a series of time periods. This method, known as dynamic linear program-

ming, is dynamic in the Hicksian sense that the factors and products are

dated.

A farming unit that considers livestock enterprises requires planning

for several years in order to achieve optimal resource efficiency. The

inclusion of multiple periods2 is necessary since some enterprises are

longer run than others. For example, two years are needed for a heifer

to become a producing cow and improved pasture requires at least two years

to reach high levels of forage production. It is important to include

multiple periods in the problem since continued changes occur in bio-

logical (such as crop rotation and livestock production), institutional

and policy constraints.


2The use of multiple periods in this study did not include the considera-
tion of time value of money. This should be included in any extension.
of the research for applications to individual producers.










There are several assumptions regarding additivity and linearity,

divisibility, finiteness and single-value expectations that are necessary

in order to use linear programming [1]. If these assumptions are not

realistic in the problem under consideration, then linear programming may

not provide a precise solution. With the assistance of these assumptions

firm theory can be transformed for use in standard linear programming

form.

Maximize profit = cx.

subject to: aij x. 0 (j = 1, 2, ..., n)


where

c = the profit from producing one unit of activity j,

x = the quantity of jth activity,

a = the technical coefficient relating the use of the ith
ij constraint in the jth activity and

bi the total amount of the ith constraint available.

The multiperiod linear programming model used in this study is an

extension of standard linear programming where the transformation from

the standard to the "dynamic" model results from the use of submatrices.

The one period standard model in vector form may be stated as

Maximize Z C'X

subject to: B > AX

X<0

where

A is a matrix of input-output coefficients,

X represents the alternative ways that factors may be trans-
formed into alternative products,









C describes the profit from each unit of the alternative pro-
ducts that may be produced and

B specifies the availability of scarce factors

The model above can easily be made "dynamic" if the input-output

matrix represents submatrices corresponding to the time periods of the

planning horizon. The overlapping in rows and columns of the submatrices

includes the time dimension to the study (Figure 2). The resources

required or produced in one time period may affect available resources or

products in some future time periods [1]. Maximum profit over time is

represented as

Profit = C X (t = 1, ..., L)
t j it jt

C.t = the profit from producing one unit of activity j during
S time period t.

The multiperiod programming matrix used in the analysis (as shown in

Figure 2) consisted of column activities, row elements, right-hand-side

constraints, resource transfers and objective function. The matrix was

constructed with the column activities across the top and the constraint

rows down the page. Each submatrix was composed of approximately 432

rows and 584 columns. The total matrix is a composite of five input-

output submatrices and resource transfers.


Coding

The large size of the multiperiod linear programming model required

a coding system to organize the numerous row elements and column activi-

ties. Code abbreviations, descriptions, constraints, right-hand-sides

and units of measurement are listed in Table 1 for the row elements of the

jth year in the dynamic linear programming model. The first three digits











































A Column identification
B Row identification
C Submatrix for year 1
D Year 1 resource transfer
E Submatrix for year 2
F Year 2 resource transfer
G Submatrix for year 3
H Year 3 resource transfer
I Submatrix for year 4
J Year 4 resource transfer
K Submatrix for year 5
L All matrix elements right of main
diagonal are zero
M Type of constraint (E = equality,
L = less than or equal, G = greater
than or equal and N = no contraint
N Right-hand-side restriction (ranges
on rows)
0 Restrictive bounds (on columns)


Figure 2. Organization of multiperiod programming input-output matrix.










were used for code abbreviations. The fpurth and fifth digits were used

to specify month and year, respectively. The remaining digits were used

in certain rows with respect to age, lactation and quality. For example,

CC02813 specified a cow transfer row in the second year where the cow

was in the eighth agegroup, was not lactating the year before and was in

the third quality group.


Objective Function

The objective function was to maximize profit for the producer over
3
the five-year planning horizon. Profit in this study was defined as the

difference in output revenues and input costs which is interpreted as the

return to land, management and other fixed factors of production.

The code abbreviation for the objective function used in the matrix

was DOLLARSI. This row was unconstrained and the unit of measurement was

dollars.


Restrictive Constraints of the Model

Factors of production, land, labor, farm manager, allotments and

operating capital, were constrained in the model. These factors were

restricted with right-hand-side constraints as indicated in Table 1. The

restrictions on dry matter, digestible protein and metabolizable energy

are entered to insure that the minimum nutritional requirements of the

beef cattle herd are met. Other row elements are used only for transfer-

ring between time periods. These constraints were used in the model to


3Producer's decisions are generally influenced by profit maximization.
However, it is recognized that some producers may have other objectives
based on custom, habit, preference, etc. that influence their production
decision.








Table 1. Code abbreviation, description, constraint and unit of measurement for row
year in the dynamic linear programming model


elements of the jth


Codea Description Constraint RHS Unit


DOLLARS

LCSij


LPS i


LRS


RLA i

ROPJ


PAL.

TAL
J


OPR.

RDMij

RDP


RME .


dollar


166.0


166.0


Objective function
th
Land available for row-crops during the i month and
jth year

Land available for pasture during the ith month and
th
j year

Land available for range during the ith month and jth
year

Labor available during the ith month and the jt year

Amount of annual operating capital available during
the jth year
th
Peanut acreage allotment during the j year
th
Tobacco acreage allotment during the j year
th
Operator or farm manager required during the j year
th th
Dry matter used during the i month and the jth year
th
Digestible protein used during the i month and the
jth year

Metabolizable energy used during the ith month and the
jth year


acre


acre


acre

hour


dollar

acre

acre
d
FM

kilogram


kilogram


0.0 megacalories


166.0

2,792.0c


100,000.0

15.0

5.0

1.0

0.0









Table 1. Continued


Codea Description Constraint RHS Unit


th th
STR Steer transfer row for the j year, K age group,
jklm Ith lactation group and mth quality group

HFR. Heifer transfer row for the j year kth age group,
jklm Ith lactation group and mth quality group

REPj Replacement heifr transfer row for the year, k
jkm age group, 1 lactation group and mt quality group
th th
YST Yearling steer transfer row for the j year, k age
klm group, 1th lactation group and mth quality group

.th th 1th
CCRm Cow transfer row for the t year, k age group,
klm lactation group and mt quality group (moves animal
into next age group)

CSG Corn production transfer corn stubble grazing for
September during the j year


Residual corn stubble transferred from September to
October during the jth year

Irrigated corn production transfer to corn stubble
grazing for September during the jth year

Residual irrigated corn stubble transferred from
September to October during the jth year

Wheat production transfer to wheat stubble grazing for
June during the jth year


0.0 megacalories


0.0


0.0


0.0


head


head


head



head


0.0 kilogram


0.0 kilogram


0.0 kilogram


0.0 kilogram


0.0 kilogram


CTS.


ICSj


ITSJ


WSG








Table 1. Continued


Codea Description Constraint RMS Unit

WTJ Residual wheat stubble transferred from June to July
during the jth year L 0.0 kilogram

WJY Residual wheat stubble transferred from July to August
during the jth year L 0.0 kilogram

WTA Residual wheat stubble transferred from August to
September during the jth year L 0.0 kilogram


aThe period was coded as the fifth digit of the eight digits in the code.
the first year and LCS05000 denoted the fifth year.


For example, LCS01000 denoted


bE = equality, L = less than or equal, G = greater than or equal and N = no constraint.

CThe amount of labor available from the farm manager each month varied by season of the
2,792 hours is the amount of labor available annually.


year [6]. The


dFM denotes a farm manager with training and experience in agricultural farm management.










reflect a realistic problem setting,


Activities of the Model

The activities of the multiperiod programming model are discussed by

categories -- field crops, forages, beef cattle and miscellaneous activi-

ties. The discussion of the activities included in these categories is

for one input-output submatrix. Table 2 presents all production activities

considered in the analysis.


Field Crops

The field crop production activities in this analysis are described

in Table 2. Each activity was entered in the matrix with the objective

function coefficient being the net return over variable cost from the

production of one unit of that activity. The variable costs of production

were inserted as the required operating capital coefficients. Other

constraining row elements, such as land, labor and allotment coefficients,

were incorporated in the matrix.


Forages

The forage production activities provide the nutritional requirements

(dry matter, digestible protein and metabolizable energy) that are neces-

sary for the production of the beef cattle enterprises. Forage output

is treated as an intermediate product where sale occurs within the beef

cattle enterprise.

The two categories of land use for forage production are cropland

and pasture. Coastal Bermuda and Argentina Bahia (perennials) activities

utilize land allocated for pasture while rye, ryegrass, millet, sorghum-

sudangrass and arrowleaf clover (annuals) are grown on cropland.







Table 2. Code abbreviation, description and unit of measurement for column activities for one sub-
matrix (one year) of the dynamic linear programming model


Codea Description Unit

PNj Peanut production activity during the jth year acre

SOY Soybean production activity during the jt year acre

SOYL. Late soybean production activity during the jt year acre
th
NWH Wheat production activity during the-j year acre

WHS Wheat stubble grazing during the ith month and the jth year kilogram

CORN. Corn production activity during the j year acre

CSi Corn stubble grazing during the ith month and the jth year kilogram

ICORN Irrigated corn production activity during the jth year acre
th th
ICSj Irrigated corn stubble grazing during the i month and j year kilogram
th

ICORNEH Irrigated corn production early harvest activity during the j year acre

TOBCH Tobacco conventional harvest production activity during the jth year acre
th
TOBMH. Tobacco mechanical harvest production activity during the j year acre

OPER. Farm manager activity during the j year FM

WRE Winter rye early production active during the year acre
WREj Winter rye early production activity during the j year acre


-~---~ `-~ -------I---------I `-----I-I










Table 2. Continued


Codea Description Unit

WRL Winter rye late production activity during the jth year acre
WRGE Winter ryegrass early production activity during the j year acre
Rth
RRGE Winter ryegrass early production activity during the j year acre
RRG Winter rye-ryegrass production activity during the year acre
WRGL Winter rye-ryegrass late production activity during the j year acre
RRGE Winter rye-ryegrass early production activity during the jth year acre





MIL Millet production activity during the jth year acre r

SSG Sorghum-sudangrass production activity during the jth year acre
th




RRGL. Winter rye-ryegrat pass late production activity during the j year acre
th




RRGC Winter rye-ryegrass-clover production activity during the j year acre





CBP Coastal Bermuda pasture production activity during the jth year acre
ABP Argentina Bahia pasture production activity during the j t year acre





HLA Hire labor activity during the ith month and the j th year hour
jth






ABRG Winter ghnegrass and Argentina ahia pasture production activity during the j year acre





ea production activity during the j year acre
ttt t tt
BPCL Arownteal Bera pasture production activity during the j year acre
th


ABP4 Argentina Bahia pasture production activity during the j year acre

HLA1. Hire labor activity during the i month and the j year hour

ABRG. Winter ryegrass and Argentina Bahia pasture production activity during
3 the jth year acre

ABCLj Argentina Bahia pasture and clover production activity during the j year acre







Table 2. Continued


Codea Description Unit

CPER. Coastal Bermuda pasture established from range production activity during
3 the jth year acre

APER. Argentina Bahia pasture established from range production activity during
the jth year acre

CPEC Coastal Bermuda pasture established from cropland production activity
during the jth year acre

APEC. Argentina Bahia pasture established from cropland production activity
during the jth year acre

HBYij Coastal Bermuda hay buy activity for the ih month and the jth year kilogram
.th th th
SSC jSell steer calf activity for the j year from the k group, 1
jm lactation group and mth quality group head

.th th th
SHCkl Sell heifer calf activity for the jth year from the k age group, 1t
lactation group and mt quality group head

SCBkl Steer production activity for the jth year from the kth age group, th
km lactation group and mth quality group head

th th
SYSkm Sell yearling steer activity for the j year from the k age group,
ith lactation group and mh quality group head

HCB jHeifer production activity for the j year from the kth age group,
jkm 1 lactation group and mth quality group head

SYH Sell yearling heifer activity for the th year from the kth age group,
jklm 1th lactation group and m quality group head










Table 2. Continued


Codea Description Unit

th
RET Retain yearling heifer (replacement) activity for the j year from the
klm kth age group, 1th lactation group and mth quality group head

SRCjm Sell for two year old replacement cow activity for the j year from the
klm kth age group, Ith lactation group and mth quality group head

th th th
CCC kl Cow production activity for the j year, k age group, 1 lactation
group and mth quality group head

th th th
SCC l Sell cull cow activity for the jh year from the k age group, 1th
m lactation group and mth quality group head

th th
CCI Cow inventory activity in the fifth year from the k age group, 1
jkm lactation group and mth quality group head



aThe period (year) was coded in the eighth digit place for row crops and forages and in the fifth
digit place for beef activities.

bFM denotes a farm manager with training and experience in agricultural farm management.










Each forage activity was entered in the matrix with the objective

function coefficient being the variable cost of production for one unit

of that activity. The operating capital coefficient was, therefore,

the same as the objective function coefficient. The constraining row

elements, such as land, labor and nutritional values, were incorporated

in the matrix.


Beef Cattle

In this analysis Melton's cow-model [4] was used and the beef cattle

herd was assumed to be of Brahman cross-breeding located in North Florida.

The beef cattle activities as described in Table 2 provide detailed
4 5
physical and biological differences in age, lactation status and quality

of the animal.6 The number of cows having calves are estimated in the

model from probabilities with respect to breed, age and whether the animal

was lactating the year before. Because of these factors the calving per-

centages vary over time.

Each beef cattle production activity was entered in the matrix with

the objective function coefficient being the carrying cost for one animal

unit of that activity. The operating capital coefficient was the same as

the objective function coefficient. Constraining row elements, such as

labor and nutritional requirements (dry matter, digestible protein and


The animals were divided into nine age groups -- 2, 3, 4, 5, 6, 7, 8-10,
11-12 and 13-18 years old.

The lactation status denotes that the animal (1) was or (2) was not
lactating the seasonal before,

The animals were divided into five quality groups as follows: 1 best,
2 good, 3 average, 4 fair, and 5 poor.










metabolizable energy), were incorporated in the matrix. The beef cattle

activities were entered as annual activities with sales occurring each

year in October.

The beef cattle sell activities were entered in the matrix with the

objective function being the total revenue from the production of one

unit of that activity. These activities did not have any constraints

placed on them. All beef cattle sell activities occur in October immedi-

ately prior to the beginning of the next production year.

Beef cattle inventory activities were used in the fifth input-output

submatrix (year 5) to allow for the retention of beef cows when their pro-

duction is profitable. Each inventory activity was entered into the

matrix with the objective function coefficient being the potential value

of that animal from continued production. The inventory value of each

animal reflected its undiscounted average future earnings from continued

production.


Miscellaneous Activities

The option to hire labor, buy hay and the requirement for a farm

manager (owner) are included in the miscellaneous activities of the model.

These activities provide the flexibility to hire labor or buy hay when

necessary and ensure that the operation has adequate management.


Results

The activities from the optimal solution that maximized profit for

the five-year planning period are presented in Tables 3 and 4. The optimal

activity levels are discussed in three categories--field crops, forages,

and beef cattle.








Table 3. Optimal activity levels for field crops and forages during the five-year planning horizon

1973 1974 1975 1976 1977 Unit

Field crops

PN 15.00 15.00 15.00 15.00 15.00 acre
SOY 36.00 40.38 23.25 22.14 76.70 acre
SOYL 9.02 28.44 acre
ICORN 0.01 0.01 0.01 0.01 acre
ICORNEH 108.74 104.36 121.49 113.58 39.60 acre
TOBMHa 5.00 5.00 5.00 5.00 5.00 acre

Forages

CBP 45.56 47.05 37.73 37.17 77.50 acre
ABP 103.87 118.95 71.28 36.31 acre
RRGEb 36.00 40.38 23.25 22.14 32.41 acre
RRGCb 9.02 13.44 acre
RRGLb 15.00 acre
ICSSc 79.01 70.24 104.50 88.69 kilogram
ICSOC 79.01 88.69 kilogram
HBY 34,741.79 39,980.03 7,278.60 19,957.44 23,378.18 kilogram


Each unit of mechanically harvested tobacco requires 1.25 acres for production.


bRye-ryegrass
cropland.


planted early, rye-ryegrass-clover and rye-ryegrass planted late are grown on


Irrigated corn stubble activities only occur when irrigated corn production activities are
in the optimal solution.










Table 4. Beef cattle inventories immediately prior


sales) in each year


Item 1972a 1973 1974 1975 1976 1977


Calves

Steers

Heifers

Yearlings

Steers

Heifers


Cows (by age)

2

3

4

5

6

7

8-10

11-12

13-18


32.50

32.50


0.00

0.00


6.70

9.20

12.00

12.90

18.40

12.90

12.00

9.20

6.70


37.74

37.4




32.50

32.50




10.00

6.70

9.20

12.00

12.90

18.40

12.90

12.00

9.20


40.82

40.82




37.74

37.74




22.46

10.00

6.70

9.20

12.00

12.68

18.16

12.66

11.81


12.60

12.60




40.82

40.82




12.16

22.46

4.48

2.07

0.62

0.59

0.00

0.00

0.00


27.41

27.41




11.12

12.60




39.15

12.16

22.46

4.48

2.07

0.62

0.45

0.00

0.00


29.19

29.19




27.41

27.41




12.60

39.15

12.16

22.46

4.48

2.07

0.62

0.45

0.00


Total cows


Calving percent


100.00 103.30 115.67


65.00


73.07


70.58


42.38 81.39 94.00

59.46 67.35 62.11


aThe 1972 inventory
distribution.


was given under the assumption of a normal age


to culling (October










The production levels of field crops were fairly consistent over time

with the exception of irrigated corn early harvest, soybeans and late soy-

beans during the latter part of the planningperiod. In 1976 and 1977

declining corn prices significantly reduced the return over variable costs

for corn and, therefore, soybeans began replacing corn in the solution

for those years. During all five years of production, mechanically har-

vested tobacco and peanuts were produced at their maximum allotted acre-

age. Shadow prices for the five years of production of mechanically

harvested tobacco and peanuts ranged from $933.30 to $1,527.30 and $11.33

to $359.66, respectively.

Forage activity levels were affected by both field crop and beef

cattle production levels. The production of winter rye-ryegrass planted

early was the least affected and the most consistently produced forage.

In 1977, however, winter rye-ryegrass-clover and winter rye-ryegrass planted

late were produced as a result of the change in field crop activities

from irrigated corn early harvest to soybeans. The change in field crops

made more cropland available to produce the lower cost winter annuals.

Marginal changes werealso reflected in 1976 from reducing the level of

irrigated corn early harvest.

During the first four years, he optimal solution specified the

utilization of Argentina Bahia pasture to help supply the nutritional

requirements of the beef cattle through the winter months since this

perennial produces some forage year round. In addition, small marginal

levels of irrigated corn stubble were also being utilized to meet the

nutritional requirements of the beef cattle herd. Forage activities

began changingin 1976, however, when corn prices decreased and soybeans










entered into the solution making cropland available through the winter

months for the production of the lower per unit cost winter annuals.

The changing inventory of the beef cattle herd also contributed to

the varying levels of forage production and Coastal Bermuda hay buy

activities. The optimal solution did not transfer any cropland or range

to pasture. The production of winter forages on cropland, however, was

preferred over pasture and pasture-ryegrass combinations to provide the

nutritional requirements through the winter months.

The initial beef cattle inventory with a normal age distribution was

assumed at the beginning of the planning horizon and the activity levels

of the beef cattle enterprises over time are presented in Table 4. The

levels of beef cattle activities varied greatly over the five years of

production as cattle prices changed.

Heifer and steer calf inventories fluctuated during the planning

horizon not only because of prices, but also due to the number of cows

in the herd and, to a lesser extent, the percent of cows having calves.

Almost all calves were transferred to yearling inventories during the

five-year production period. The heifer and steer yearling activities

entered into the solution primarily due to the efficient rates of gain

made during their growing stage in this activity. In 1976, however, all

steer calves were not transferred to the yearling steer activities since

the higher quality steer calves were sold in 1975. The heaviest steer

calves produced were sold because the factor cost of supplying their

higher nutritional requirements exceeded their marginal value product

during the yearling activity.

The cow production activities changed dramatically during the five-










year production period as a result of changes in cattle prices. During

1973 and 1974 there was a buildup in the cow inventories while profits

were being realized at all levels of production. At the end of 1974,

however, the beef cattle herd was reduced to those animals of the highest

quality in the first six age groups. Throughout the rest of the planning

horizon, the beef cattle herd increased in size along with increasing

product prices.

The input costs and output revenues for the optimal activity levels of

field crops are presented in Table 5. The average annual product prices

were used for each period [6]. Yields were assumed constant over the

five-year planning horizon.

The input costs for field crops exhibited a gradual increase except

in the fifth year where the optimal solution reduced irrigated corn pro-

duction early harvested (which had a large input cost associated with its

production) and increased soybean activity levels (that required lower

amounts of operating capital). In general, however, input costs increased

during the study period.

Output revenue was variable over time due to fluctuating product

prices. The highest field crop revenue occurred in 1974 when both corn

and soybean prices were at their highest level during the planning period.

The output revenues produced by mechanically harvested tobacco and peanuts

were the most consistent over time because of slightly increasing product

prices. The smallest output revenue recorded during the production

period was $42,499.34 in 1977, that resulted primarily from low corn prices.

The input costs and optimal forage activity levels for each of the

five years are described in Table 6. The optimal forage activity levels










Table 5, Input costs and output revenues for optimal field crop
activities for each of the five years


Year Column Activity Input costs Output revenue


1973


PN
SOY
ICORN
ICORNEH
TOBMH


15.00
36.00
0.01
108.74
5.00


1974


2,604.15
2,224.63
1.10
11,363.57
3,473.50

" 19,666.91


2,960.85
2,837.03
1.11
12,399.21
3,949.30

22,147.50


3,246.30
1,791.03
1.81
15,825.86
4,329.95

25,194.95


3,460.35
1,817,63
740.68
16.34
15,771.86
4,615.45

26,422.31


3,567.30
6,492.88
2,407.70
5,669,36
4,758.20

22,895.44


PN
SOY
ICORN
ICORNEH
TOBMH


1975


PN
SOY
ICORN
ICORNEH
TOBMH


7,626.00
4,881.23
2.94
30.502.21
9,240.00

52,252.38


8,370.00
7,074.41
3.42
38,405.09
10,605.00

64,457.92


9,253.50
2,455.31
4.12
36,081.07
10,237.50

58,031.50


9,486.00
3,718.95
1,262.89
33.66
32,484.18
11,497.50

58,483.18


9,625.50
10,124.75
3,128.73
6,970,36
12,600,00

42,449.34


15.00
40.38
0.01
104.36
5.00


15.00
23.25
0.01
121.49
5.00


15.00
22.14
9.02
0.01
113.58
5.00


15.00
76.70
28.44
39.60
5.00


1976


PN
SOY
SOYL
ICORN
ICORNEH
TOBMH


PN
SOY
SOYL
ICORNEH
TOBMH


1977











Table 6. Input costs and optimal forage activities for each of the
five years


Year Column Activity Input costs


1973


11,978.17


CBP
ABP
RRGE
HBY


45.56
103.87
36.00
34,741.79


1974


CBP
ABP
RRGE
HBY


1975


CBP
ABP
RRGE
HBY


2,440.95
5,565.22
1,929.45
1,987.23

11,922.85


2,866.03
7,246.69
2,460.70
2,598.70

15,172.12


2,519.75
4,760.84
1,553.40
518.96

9,352.95


2,646.61
2,585.11
1,576.57
654.45
1,516.77

8,979.51


5,688.32
2,379.64
1,005.40
1,101.30
1,803.51


47.05
118.95
40.38
39,980.03


37.73
71.28
23.25
7,278.60


37.17
36.31
22.14
9.02
19,957.44


77.50
32.41
13.44
15.00
23,378.17


1976


1977


CBP
ABP
RRGE
RRGC
HBY


CBP
RRGE
RRGC
RRGL
HBY











and input costs for forages varied significantly due to the changing

size and structure of the beef cattle herd.

The beef cattle sold in each year by age are summarized in Table 7.

The number of animals that were sold reflects the changes in the optimal

beef cattle inventories presented in Table 4.

In 1975, the highest quality steer calves were sold since there factor

costs would have exceeded their marginal value product during the yearling

activity, while the rest of the lower quality steer calves were kept and

transferred into the yearling steer activity. During other years, how-

ever, the heifer and steer calves were transferred to yearling activities

except in 1977 when the heifer and steer calves were liquidated since the

model did not provide for future production (inventory) of these activities.

Yearlings were sold in every year. The steer yearlings, however,

were required to be sold since beef finishing activities were not speci-

fied. Heifer yearlings, though, were allowed to be either kept as replace-

ments for the beef cattle herd or sold at the end of the yearling activity.

During the first two years of the production period only the higher

quality heifer yearlings were kept as replacements to build the beef cattle

herd. In the fifth year all yearling heifers were liquidated.

In 1973 cows were culled primarily due to age as indicated in the

13-18 year old age group. Other animals culled in that year were poor

quality animals that were not lactating the year before. In the second

year (1974), all animals seven years old and older were removed from the

herd and only the best quality animals in the other age groups were

retained for future production. During the last two years of the planning

period no cows were sold as the beef cattle herd was in a rebuilding











a
Table 7. Beef cattle sold in each year by age


Item 1973 1974 1975 1976 1977

Calves

Steers 0.00 0.00 1.48 0.00 29.19

Heifers 0.00 0.00 0.00 0.00 29.19


Yearlings

Steers 32.50 37.74 40.82 11.12 27.41

Heifers 10.04 25.58 1.67 0.00 27.41


Cows (by age)

2 0.00 0.00 0.00 0.00 0.00

3 0.00 5.52 0.00 0.00 0.00

4 0.00 4.63 0.00 0.00 0.00

5 0.00 8.58 0.00 0.00 0.00

6 0.22 11.41 0.14 0.00 0.00

7 0.24 12.68 0.00 0.00 0.00

8-10 0.24 18.16 0.00 0.00 0.00

11-12 0.19 12.66 0.00 0.00 0.00

13-18 9.20 11.81 0.00 0.00 0.00

Total cows 10.09 85.45 0.14 0.00 0.00


aThe assumption of divisibility allows fractional units of beef cattle
to be sold in October of each year.












period as a result of increasing prices,

Input costs and output revenues associated with the optimal beef

cattle activities are presented in Table 8 for each production year.

The data supporting these input costs and output revenues were presented

in Tables 4, 6, and 7.

Because of fluctuating prices and the changing structure of the herd,

beef cattle output revenues varied drastically over time. The largest

revenue, $56,493.81, occurred in 1974 when the herd was severely culled in

anticipation of the low beef cattle prices the following year. The

lowest output revenue occurred in 1976 because of small herd size resulting

from previous culling and because all yearling heifers were retained in

the herd in that year.

The fluctuations in input costs for the beef cattle herd were similar

to the fluctuations in beef cattle output revenues, although not nearly

as drastic. The input costs for forage and hay and animal carrying

increased steadily over time on a per unit basis. The size and structure

of the beef cattle herd played a major role indetermining the costs of

production.

The production from the beef cattle herd resulted in output revenues

greater than input costs in all years except 1976. Only in 1974 was

there more than an average return on beef cattle enterprises. It should

be understood, though, that 1976-77 were years of extremely low beef

cattle prices.

Profit and loss statements for each year in the planning period are

presented in Table 9. It is important to realize that only variable

costs have been included in calculating profit. Therefore, profit should







Table 8. Input costs and output revenues for optimal beef cattle activities for each of the
five years


1973 1974 1975 1976 1977


Revenue

Calf sales

Steers
Heifers

Yearling sales


Steers
Heifers


Cull cow sales
all ages

Total revenue


10,846.78
2,669.52


2,885.64

16,401.94


16,659.67
9,289.11


30,545.03

56,493.81


209.42


11,215.80
379.74


4,370.14
3,608.57


2,408.19


8,007.26
5,961.19


43.96


11,848.92


2,408.19


21,947.16


Costs


Forage and hay
Cow carrying
Yearling carrying


11,922.86
1,387.32
427.05


15,172.12
1,766.36
563.88


9,352.96
711.59
668.59


8,979.51
1,452.66
207.05


17,502.36 10,733.14 10,639.22


12,005.17
1,729.25
493.29

14,227.71


Total input costs 13,737.23









Table 9. Profit and loss statements for each year of the planning horizon


1973 1974 1975 1976 1977 Averagea

Revenue

Field crops 52,252.38 64,457.92 58,031.50 58,483.17 42,449.34 55,134.86
Beef cattle 16,401.94 56,493.81 11,848.92 2,408.19 21,947.16 21,820.00

Total Revenue 68,654.32 120,951.73 69,880.42 60,891.36 64,396.50 76,954.86


Costs

Field crops 19,666.94 22,147.50 25,194.95 26,422.32 22,895.44 23,265.43
Beef cattle 13,737.23 17,502.36 10,733.14 10,639.22 14,227.71 13,367.93
Operator 8,760.00 9,960.00 10,920.00 11,640.00 12,000.00 10,656.00


Total Costs 42,164.17 49,609.86 46,848.09 48,701.54 49,123.15 47,289.36


Profit 26,490.15 71,341.87 23,032.33 12,189.82 15,273.35 29,665.50


aColumns and rows may not sum due to rounding differences.


bProfit is interpreted as the return to land, management and other fixed factors of production.












he interpreted as the return to land, management and other fixed factors

of production.

Total revenues from all production activities were moderately consis-

tent over time except in 1974 when field crop product prices were high

and a large percentage of the beef cattle herd was liquidated because of

anticipated decreasing product prices. The total revenues from field

crops were consistently greater than beef cattle revenues. In general,

field crop revenues averaged 72 percent of the total revenue generated.

Beef cattle revenues ranged from 4 percent to 47 percent of the annual

total revenues produced.

The total costs of producing were much less variable over the pro-

duction period than total revenue. During the five years of production

field crop costs represented 49 percent of the average cost of production

while beef cattle enterprises incurred 28 percent and the farm operator

accounted for 23 percent of the average cost of production.

All activities for the five years of production resulted in a profit

of $148,327.50. Beef cattle and field crops both played a major role

in generating this profit.

The largest profit occurred in 1974 when field crop product prices

were high and much of the beef cattle herd was liquidated. In 1976, how-

ever, the lowest profit was recorded due to low field crop and beef

cattle prices, and all yearling heifers were retained for rebuilding the

beef cattle herd.

The average annual profit during the five years of production was

$29,665.50. The profit over time was highly variable reflecting the

composite of high and low profit years for both beef cattle and field











crops. The annual profit ranged from 8 percent to 48 percent of the total

profit for the five-year production period.


Summary

The major purpose of this study was to develop a profit maximizing

model to determine the optimal resource organization of field crop and

beef cattle producers in North and West Florida. The resource situations

on field crop and beef cattle farms were defined and estimates obtained

for (1) costs and returns associated with selected field crops, (2) costs

and returns associated with selected beef cattle enterprises, (3) costs

of production and nutritional coefficcints for potential forage crops

of the area and (4) nutritional requirements associated with selected

beef cattle.

A profit maximizing dynamic linear programming model was developed

to determine the optimal levels of field crops, forage and beef cattle

enterprises. The constraints included in the model were (1) land, (2)

labor, (3) operating capital, (4) tobacco and peanut allotments, (5) farm

manager, (6) dry matter, (7) metabolizable energy and (8) digestible

protein. This model was used to develop the optimal organization of

farm resources given prices over a five-year planning horizon, 1973-77.

The optimal resource organization, given price levels that existed

during the 1973-77 period, included producing a combination of field crops,

forages and beef cattle enterprises. The production levels of these

activities varied directly with product prices over the planning horizon.

Field crops included in the solution were flue-cured tobacco, peanuts,

irrigated corn, irrigated corn early harvest, soybeans and late soybean

production. Flue-cured tobacco and peanuts were consistently produced at

the upper limits of their allotments. The production levels of corn and











soybean activities varied over the planning horizon with product prices,

Forage activities in the solution included coastal bermuda pasture,

Argentina Bahia pasture, winter rye-ryegrass planted early and late, irri-

gated corn stubble (September and October), winter rye-ryegrass-clover

and Coastal Bermuda hay buy. Forage activity levels varied during the

five years of production due to the variation in field crop and beef

cattle activity levels.

The optimal beef cattle activities in the solution included calves,

yearlings and all ages of beef cows. The structure of the beef cattle

herd changed dramatically during the planning period with variations in

cattle prices. The size of the beef cattle herd ranged from 42 to 116

animals over the five years.

These activities produced an average yearly profit of $29,665.50

over the five-year planning horizon (1973-77). Profit was defined in

this study as the difference in output revenues and input costs which also

may be interpreted as the return over variable cost to land, management

and other fixed factors of production.

The highest profit occurred in 1974 when field crop product prices

were high and numerous beef cattle were liquidated from the herd. The

smallest profit was recorded in 1976 due to low field crop and beef

cattle prices and a large number of replacement heifers were retained for

the beef cattle herd. Profit per year ranged from 8 percent to 48 per-

cent of the total profit obtained during the five-year production period.


Limitations

Before adapting the model or extending the results, specific limita-

tions must be recognized within the analysis. The resource situation,











production estimates and costs and model assumptions are limitations that

cannot be generalized for all situations and provide reliable results,

In this analysis a specific resource situation was defined in the

model. Among producers and farms the available resources vary greatly.

It is important to recognize the quantity of resources available because

they form the constraints on production.

Production estimates vary with respect to the level of inputs and

may also vary among producers and farms. It is necessary for one to

realize that each level of production represents a different point on

the production function. With given factor and product prices only one

level of production maximizes profit.

The assumptions of the dynamic linear programming model may be

considered limiting. These assumptions are additivity and linearity,

divisibility, finiteness and single-value expectations. If these assump-

tions do not hold, the results obtained from this. model may not reflect

maximum profit. These and other possible limitations, such as risk con-

siderations, should be considered before drawing conclusions from the

results. Recognizing the limitations of the model makes the user aware

of the necessary improvements that would contribute more accuracy and

preciseness to the model. The model in its present form, however, has

many potential uses. Given the appropriate data set, the model has the

flexibility to analyze any size of an agricultural operation and any

combination of enterprise activities and constraints.


Need for Further Research

It is believed that this study constitutes the first such analysis to










combine the production of field crops, forages and beef cattle enter-

prises in a dynamic linear programming framework, As a pioneering study

it is obvious that further methodological refinements might be useful if

this analysis is to be used as a basis for firm level decision making.

Additional research is needed on (1) defining the resource situation,

(2) production estimates and costs and (3) limitations of the model

assumptions that may be sensitive to the analysis. For example, cropland

and pasture may each be separated into different levels of production

which will more accurately specify the available resource situation.

Future research efforts should consider the time value of money,

maximizing net worth and/or incorporating tax considerations from the

Internal Revenue Code in the model to maximize after tax profit. The

inclusion of a cash flow summary and investment activities would also

contribute added flexibility. In addition, the responsiveness of the

model to imbedded price fluctuation is adequate testimony to support

the need for improved price forecasting procedures if such rigorous

techniques are ever to become widely used at the farm level.

With these and other refinements, more detailed information from

the optimal farm resource organization can be provided at the firm level

for decision making. It is obvious that organizational changes in

agriculture will occur with or without prior research. An adequate base

of research results upon which informed decisions can be made, however,

will improve the chances of realizing organization changes that yield

efficient food and fiber production,











References


[1] Heady, E. 0. and W. Candler, Linear Programming Methods, Iowa State
College Press, Ames, 1958,

[2] Henderson, James M. and Richard E. Quandt, Microeconomic Theory,
Second edition, McGraw-Hill, Inc. New York, 1971.

[3] Loftsgard, Laurel D. and Earl 0. Heady. "Application of Dynamic
Programming Models for Optimum Farm and Home Plans," Journal of
Farm Economics 41:51-62, February, 1959.

[4] Melton, Bryan E. "Nutrient Requirements and Least-Cost Supplement
Rations for Florida Beef Cow Herds," University of Florida, Food
and Resource Economics Department,. Economic Report 94, Gaines-
ville, December, 1978.

[5] Prevatt, James W. "Optimal Farm Resource Organization for North and
West Florida: An Application of Dynamic Linear Programming."
Unpublished Master's Thesis, University of Florida, Gainesville,
1979.

[6] Prevatt, J. Walter, John E. Reynolds, and Bryan E. Melton. "Budgets
for Selected Field Crop, Forage and Beef Cattle Enterprises in
North and West Florida, 1977." Economic Information Report 121,
Food and Resource Economics Department, Gainesville, 1979.

[7] Tyner, F. H. The Changing Economic Structure of North and West Florida,
Department of Agricultural Economics, Agricultural Economics
Report No. 17, Gainesville, March, 1971.

[8] University of Florida. Florida Statistical Abstract, 1976, Tenth
Annual Edition, Bureau of Economic and Business Research,
College of Business Administration, University of Florida Press,
Gainesville, 1977.




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