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Unformatted text preview: 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: ________________________________________ 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 3...
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This note was uploaded on 12/24/2011 for the course AAEC 5024 taught by Professor Taylor,d during the Fall '08 term at Virginia Tech.
- Fall '08
- The Land