Economics Report 102
An Optimal Farm Enterprise
North and West Florida
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
Bryan E. Melton
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 . . . .
. . . .
. . .. ..
LIST OF TABLES
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
1 Planning Districts, I, II, and III in North and 2
West Florida . . . . .
*2 Organization of multiperiod programming activity 7
matrix . . . . . .
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 . 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 .
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
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
Figure 1. Planning Districts I, II, and III in North and West Florida.
j/ ^ ^
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 .
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 .
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 . 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 . These functions are
used to achieve the optimal level of production that will maximize profit.
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  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
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 . 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
Maximize profit = cx.
subject to: aij x. 0 (j = 1, 2, ..., n)
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
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 . Maximum profit over time is
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.
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
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.
The objective function was to maximize profit for the producer over
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
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
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
Land available for row-crops during the i month and
Land available for pasture during the ith month and
Land available for range during the ith month and jth
Labor available during the ith month and the jt year
Amount of annual operating capital available during
the jth year
Peanut acreage allotment during the j year
Tobacco acreage allotment during the j year
Operator or farm manager required during the j year
Dry matter used during the i month and the jth year
Digestible protein used during the i month and the
Metabolizable energy used during the ith month and the
Table 1. Continued
Codea Description Constraint RHS Unit
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
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
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 . 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.
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.
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
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
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
ICSj Irrigated corn stubble grazing during the i month and j year kilogram
ICORNEH Irrigated corn production early harvest activity during the j year acre
TOBCH Tobacco conventional harvest production activity during the jth year acre
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
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
RRGL. Winter rye-ryegrat pass late production activity during the j year acre
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
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
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
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
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
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.
In this analysis Melton's cow-model  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
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
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.
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
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
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.
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
Cows (by age)
100.00 103.30 115.67
42.38 81.39 94.00
59.46 67.35 62.11
aThe 1972 inventory
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
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 . 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
Table 6. Input costs and optimal forage activities for each of the
Year Column Activity Input costs
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
Table 7. Beef cattle sold in each year by age
Item 1973 1974 1975 1976 1977
Steers 0.00 0.00 1.48 0.00 29.19
Heifers 0.00 0.00 0.00 0.00 29.19
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
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
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
1973 1974 1975 1976 1977
Cull cow sales
Forage and hay
17,502.36 10,733.14 10,639.22
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
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
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
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.
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
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.
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,
 Heady, E. 0. and W. Candler, Linear Programming Methods, Iowa State
College Press, Ames, 1958,
 Henderson, James M. and Richard E. Quandt, Microeconomic Theory,
Second edition, McGraw-Hill, Inc. New York, 1971.
 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.
 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.
 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,
 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.
 Tyner, F. H. The Changing Economic Structure of North and West Florida,
Department of Agricultural Economics, Agricultural Economics
Report No. 17, Gainesville, March, 1971.
 University of Florida. Florida Statistical Abstract, 1976, Tenth
Annual Edition, Bureau of Economic and Business Research,
College of Business Administration, University of Florida Press,