1. With Vegetable Farm Example
Extra LP Notes
With Vegetable Farm Example

2. 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?

3. Background: Enterprise Combinations
Economic theory behind whole-farm
planning.

4. 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.

5. Graph of PPC
enterprise 2
enterprise 1

6. Types of Enterprise Relationships
Competitive with constant substitution
Competitive with increasing substitution
Supplementary
Complementary

7. Competitive with Constant Substitution
enterprise 2
These enterprises use
the same inputs, in the
same ratios.
enterprise 1

8. Competitive with Increasing Substitution
enterprise 2
The enterprises use different
ratios of inputs and inputs
experience diminishing
marginal returns in each case.
enterprise 1

9. Supplementary enterprise 1 makes use of some inputs that are not
needed for enterprise 2
enterprise 2
supplementary range
enterprise 1

10. Complementary enterprise 2 as we produce more of
enterprise 1, we can also
produce more of
enterprise 2
enterprise 1

11. Examples Competitive Constant Sub: corn and milo
Competitive Increasing Sub:
Supplementary:
Complementary
corn and milo
corn and cotton
soybeans and winter stockers
broilers and cattle

12. Terms Physical substitution ratio: Quantity of Output Lost
Profit Ratio
Quantity of Output Lost
Quantity of Output Gained
Profit per unit of gained output
Profit per unit of lost output

13. Physical Substitution Ratio
The physical substitution ratio is the slope
of the Production Possibility Curve.

14. 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.

15. Decision Rule
Physical Substitution Ratio =
Price Ratio

16. Graph: Point of Tangency
enterprise 2
isoprofit lines and PPC
enterprise 1

17. In real life We don't know the PPC. We are going
to approximate this process using a
technique called "Linear Programming."

18. 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.

19. Returns over variable costs
The returns over variable costs come from
the enterprise budgets.

20. Farm Planning Process Inventory available resources
Select enterprises to be considered.
Obtain appropriate Enterprise Budgets.
Figure out the "technical coefficients" and "RHS" (limits)
Develop linear programming tableau.
Find optimal enterprise combination.

21. 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.

22. 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.

23. Restrictions in LP Each limited resource requires one
linear restriction in the LP model. They
are normally "inequality constraints."

24. 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.

25. Marketing Restrictions
Marketing: The local market will absorb
no more than the output of:
16 beds of tomatoes
8 beds of lettuce

26. 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.

27. Setting up the LP: Objective Function
 = 1 Y1 + 2 Y2
Y1 is the number of tomato beds
Y2 is the number of lettuce beds
 = 40Y Y2

28. Restrictions Y1 ≤ 16 (marketing restriction for tomatoes)
Y2 ≤ 8 (marketing restriction for lettuce)
Y1 + 2Y2 ≤ (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.

29. All Together in Equation Form
Objective max 40Y Y2 = 
Subject to:
Y ≤ 16
Y2 ≤ 8
Y Y2 ≤ 24

30. Graphing the constraints
lettuce
(mktg 1) 12
(labor) 8
(mktg 2) 24 16
tomatoes

31. Creating The "PPC" lettuce (mktg 1) 12 (labor) 8 (mktg 2) 24 16
Feasible Region 24 16
tomatoes

32. Feasible Region
lettuce
(8,8) 8
Feasible Region
(16,4) 16
tomatoes

33. Optimizing: Max profit $760
lettuce
isoprofit lines
slope = -30/40
Profit-Max Combination
(16,4) 8
Feasible Region 16
tomatoes

34. 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.

35. Equation Form Again Objective max 40Y1 + 30 Y2 =  Subject to: Y1 ≤ 16

36. The LP "tableau" Y1 Y2 Type RHS OBJ 40 30 MT1 1 0 LE 16 MT2 0 1 LE 8
LBR LE 24
Where LE means less than or equal to and
RHS stands for "right hand side"

37. The RHS The RHS (right-hand side) contains the
amount of the constrained resource you
have available.

38. Technical Coefficients
The numerical values in the constraint rows,
other than the RHS entries, are the
technical coefficients.

39. 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.

40. Using Excel to Solve the LP
I took the tableau for the vegetable example, and solved it using Excel Solver (a tool in Excel). I get the answers 16 beds of tomatoes, 4 beds of lettuce, and profit of $760. If you pop this page open, you can see the formulas I used. You'll learn how to use Solver in the following
slides.