1
AAEC 5024
Name _________________________
Fall 2009
D. B. Taylor
December 11, 2009
FINAL EXAM
There are a total of 100 points on the exam, with the point values of the questions (and their
sub-parts as appropriate) located in parentheses.
There is a time limit on the exam.
Time
and energy may be your most binding constraints, so use your time appropriately to
maximize the points that you earn on the exam.
Remember that I am as, or more,
interested in how you get an answer as I am in you doing all of the mathematics correctly.
If you make a mistake and are running out of time and/or energy, but you need an answer
to go on with the problem, do the following: (1) take your wrong answer (tell me that you
know that it is wrong, and why you know that it is wrong), or (2) make up an answer (tell
me that you made up the answer and why you did), and (3) continue with the problem.
You must turn in this copy of the questions with your answers in order to obtain any
credit for the exam.
Also, you must sign the pledge at the bottom of this cover sheet to
receive credit for the exam.
Pledge:
I have neither given nor received unauthorized assistance on this exam.
Signature:
________________________________________

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2
1. (56) Consider the following problem for a small holder farmer.
a) (40) A Ugandan farmer wants you to develop a profit maximizing linear
programming model for his farm.
The following table lists the crops that he
grows, their cost, yields and market price.
Be sure to clearly define all of your
decision making variables.
Do not do any intermediate calculations with the
information in the following table to develop coefficients for the model if you
want to receive full credit for your answer.
Crops
Costs (excluding
labor) per acre
Yields Per Acre
(Units)
Market Price
Per Unit
Labor
required per
acre (person
days)
Maize
monocropped
5,000
11 bags
1,000 per bag
10
Maize
intercropped with
Cowpeas
2,225
6 bags
1,000 per bag
6
Cowpeas
monocropped
8,000
14 bags
1,200 per bag
12
Cowpeas
Intercropped with
Maize
4,500
8 bags
1,200 per bag
7
Groundnuts
monocropped
10,000
15 bags
2,000 per bag
20
Coffee
monocropped
20,000
20 bags
5,000 per bag
40
Bananas
monocropped
15,000
25 bunches
3,000 per
bunch
60
Coffee
intercropped with
bananas
11,000
11 bags
6,000 per bag
22
Bananas
intercropped with
coffee
8,000
20 bunches
3,000 per
bunch
35
A person day of labor costs 500.
The farmer has access to 20 acres of land.
However at any given time, 5 of those acres are in bush fallow. The farmer has
150 person days of unpaid family labor available and will have to hire any
additional labor needed for his crop production.
While rotations are not normally
employed because of the fallow land, the farmer wants the model to evaluate the
profitability of growing monocrop maize and monocrop groundnuts (one year of
groundnuts to two years of maize) in rotation as well as growing them without a
rotation.
Due to food security concerns, the farmer wants to produce at least 6
bags of cowpeas, 10 bags of maize, 5 bags of groundnuts, and 180 bunches of