WholeFarm Planning

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Unit 3

• Whole-Farm Planning

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Whole Farm Planning
Whole-farm planning is largely a matter of
enterprise selection. What crops and livestock
enterprises will be produced on this farm in the
next year?
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Background Enterprise Combinations
Economic theory behind whole-farm planning.
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Production Possibility Curve
Definition A Production Possibility Curve (PPC)
is the geometric representation of the
combination of products that can be produced with
a given set of inputs. It can be defined for an
entire economy or for a single firm.
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Graph of PPC
enterprise 2
enterprise 1
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Types of Enterprise Relationships

• Competitive with constant substitution
• Competitive with increasing substitution
• Supplementary
• Complementary

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Competitive with Constant Substitution
enterprise 2
These enterprises use the same inputs, in
the same ratios.
enterprise 1
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Competitive with Increasing Substitution
enterprise 2
The enterprises use different ratios of inputs
and inputs experience diminishing marginal
returns in each case.
enterprise 1
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Supplementary
enterprise 1 makes use of some inputs that are
not needed for enterprise 2
enterprise 2
supplementary range
enterprise 1
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Complementary
enterprise 2
as we produce more of enterprise 1, we can also
produce more of enterprise 2

enterprise 1
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Examples
Competitive Constant Sub Competitive Increasing
Sub Supplementary Complementary
corn and milo
corn and cotton
soybeans and winter stockers
broilers and cattle
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Terms

• Physical substitution ratio
  
• Profit Ratio

Quantity of Output Lost Quantity of Output Gained
Profit per unit of gained output Profit per unit
of lost output
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Physical Substitution Ratio
The physical substitution ratio is the slope of
the Production Possibility Curve.
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Profit Ratio
Profit Ratio is the slope of the isoprofit
line ? ?1 Y1 ?2 Y2
where ?1 is profit per unit of enterprise 1, Y1
is the number of units (e.g. acres) produced,
?2 is the profit per unit of enterprise 2 and Y2
is the number of units produced.
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Decision Rule
Physical Substitution Ratio Price Ratio
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Graph Point of Tangency
enterprise 2
isoprofit lines and PPC
enterprise 1
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In real life
We don't know the PPC. We are going to
approximate this process using a technique called
"Linear Programming."
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Linear Programming
Linear programming maximizes or minimizes a
particular linear objective function, subject to
linear restrictions. Here our objective function
is to maximize the returns over variable costs.
This is a one-year or short-run plan.
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Returns over variable costs
The returns over variable costs come from the
enterprise budgets.
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Farm Planning Process

• Inventory available resources
• Select enterprises to be considered.
• Prepare Enterprise Budgets.
• Figure out the "technical coefficients."
• Develop linear programming tableau.
• Find optimal enterprise combination.

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Resource Inventory
The resource inventory tells you how much of each
resource (e.g. land, labor, other inputs) you
have on the farm. Labor resources is usually
calculated for several periods of the year. Land
may be of several different types.
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Technical Coefficients
Technical Coefficients tell you how much of each
resource you need to produce one unit of a given
enterprise. For example, it takes one acre of
row-crop land to produce one acre of cotton.
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Restrictions in LP
Each limited resource requires one linear
restriction in the LP model. They are normally
"inequality constraints."
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Consider a simple example
Vegetable production in Zaire. Possible
enterprises Lettuce and tomatoes. Each bed of
lettuce makes a profit of 30 "Zaires" (local
currency). Each bed of tomatoes makes a profit
of 40 Zaires.
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Marketing Restrictions
Marketing The local market will absorb no more
than the output of 16 beds of tomatoes 8 beds
of lettuce
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Labor Restriction
The student who wants to grow vegetables can work
up to 24 hours per week on his garden.
Tomatoes require 1 hour per week. Lettuce
requires 2 hours per week.
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Setting up the LP Objective Function
? ?1 Y1 ?2 Y2
Y1 is the number of tomato beds Y2 is the number
of lettuce beds
? 40Y1 30 Y2
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Restrictions
Y1 ? 16 (marketing restriction for
tomatoes) Y2 ? 8 (marketing restriction for
lettuce) Y1 2Y2 ? 24 (labor) So we can
produce no more than 16 beds of tomatoes and 8
beds of lettuce. And we must limit our labor so
that the amount expended is less than 24 hours
per week.
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All Together in Equation Form
Objective max 40Y1 30 Y2 ? Subject to
Y1 ? 16
Y2 ? 8 Y1 2Y2 ? 24

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Graphing the constraints
lettuce
(mktg 1)
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(labor)
(mktg 2)
8
24
16
tomatoes
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Creating The "PPC"
lettuce
(mktg 1)
12
(labor)
(mktg 2)
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Feasible Region
24
16
tomatoes
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Feasible Region
lettuce


(8,8)

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Feasible Region
(16,4)
16
tomatoes
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Optimizing Max profit 760
lettuce
isoprofit lines slope -30/40
Profit-Max Combination


(16,4)


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Feasible Region
16
tomatoes
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With more enterprises
With more than two enterprises, we can't graph
the solution. We will use some software to find
our answer. First we must put the problem in
proper form.
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Equation Form Again
Objective max 40Y1 30 Y2 ? Subject to
Y1 ? 16
Y2 ? 8 Y1 2Y2 ? 24

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The LP "tableau"
Y1 Y2 Type RHS
OBJ 40 30 MT1 1
0 LE 16 MT2 0
1 LE 8 LBR 1 2
LE 24 Where LE means less than or equal to
and RHS stands for "right hand side"
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The RHS
The RHS (right-hand side) contains the amount of
the constrained resource you have available.
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Technical Coefficients
The numerical values in the constraint
rows, other than the RHS entries, are the
technical coefficients.
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Objective Function
The values in the OBJ row are the amount of
profit per unit of enterprise produced. In your
farm plan, you will get these values from the
Enterprise Budgets. For your OBJ values Use
Returns above Variable Costs.
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Another Example
You have 3 possible enterprises on the farm
corn, cotton, and soybeans. Enterprise budgets
for these three crops are available from ACES
(see hand out).
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Restrictions

• land 300 acres total
• labor 400 hours total per 2-month period
• machinery (cotton) limit of 200 acres.

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Putting together the tableau

• use the enterprise budgets
• the information on resource limits
• the labor requirements hand out

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Cotton Corn Soy RHS OBJ 130.82
74.71 79.43 -- Land 1
1 1 LE 300 Lab2 0.8
1.3 0.5 LE 400 Lab3
2.0 0.4 1.7 LE 400
Lab4 0.5 0 0
LE 400 Mach 1 0 0
LE 200
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Step 1 Enter Data
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step 2, add "used" column and "answers row"
SUMPRODUCT(B3D3,B9D9) formula in this cell
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Copy and Paste this formula
SUMPRODUCT(B6D6,B9D9) Formula in cell G6
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Answer
175 acres cotton, 125 acres corn. Returns above
VC 32,232.25
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Sensitivity Report
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Interpreting this Report
Reduced Cost is the amount that net returns would
fall if one acre of an unselected enterprise were
produced. Shadow price is the amount the
objective function would increase if one more
unit of a limited resource were available.
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Notice
If an enterprise enters the solution (is selected
for the farm plan), it has no reduced cost. Only
enterprises not in the solution have a reduced
cost. If a resource is not completely used
up, it has a shadow price of 0. If you have
some resource left over, unused, you wouldn't
want to buy more of it.
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Shadow Price
Shadow price is the MVP of the limited resource.
If the MVP is greater than the cost of getting
another unit, you will want to get more of this
resource.