# A farmer has 1000 acres of land on which he can grow corn, wheat and soybean….

MBA Program

INDIVIDUAL ASSIGNMENT 1 for analytical DECISION MODELLING FOR BUSINESS DECISIONS

• Develop a linear programming model for each of the following problems.
1. A farmer has 1000 acres of land on which he can grow corn, wheat and soybean. Each acre of corn costs birr 100 for preparation, requires 7 man-days work and yields a profit of birr 30. An acre of wheat costs birr 120 to prepare, requires 10 man-days of work and yields a profit of birr 20. An acre of Soybeans costs birr 70 to prepare, requires 8 man-days of work and yields a profit of birr 20. If the farmer has birr 100,000 for preparation and can count on 8000 man-days of work, how may acres should be allocated to each crop to maximize profit?

2. A firm has produced three products A, B, and C. Each of which passes through three departments: Fabrication, finishing, and packaging. Each unit of product A requires 3,4, & 2 hours; a unit of B requires 5,4, and 4 hours while each unit of product C requires 2,4 and 5 hours respectively in three departments. Every day, 60 hours are available in the fabrication departments, 72 hours in the finishing department and 100 hours in the packaging department. If the unit contribution of product A is birr 5, of product B is 10 and of product C is birr 8, determine the number of units of each of the products, that should be made each day to maximize the total contribution.

3. Dinsho Company sells two types of fertilizers, Urea and DAP. Urea fertilizer contains 2 units of chemical A and 4 units of Chemical B per sack and the DAP fertilizer contains 3 units of each of the chemical A and B per sack. Urea and DAP fertilizers sell at \$3 and \$4 per sack respectively. A farmer requires at least 90 units of chemical A and at least 120 units of chemical B for his farm. How many of each fertilizer should the farmer purchase to minimize the cost while meeting the requirement?

4. An air force is experimenting with three types of bombs P, Q, and R in which three kinds of Explosive viz, A, B and C will be used. Taking the various factors into consideration, it has been decided to use the maximum 600 kg of explosive A, at least 480 kg of explosive B and Exactly 540 of explosive C. Bomb P requires 3,2,2 kg of A,B,C respectively. Bomb Q requires 1, 4, 3 kg of A, B, and C respectively. Bomb R requires 4, 2, 3 kg of A, B, C respectively. Now bomb P will give the equivalent of 2 ton explosive, bomb Q will give 3 ton explosive and bomb R will give 4 ton explosive. Under what production schedule can the Air Force make the biggest bang?

5. A firm has an advertising budget of birr 720,000. It wishes to allocate this budget to two media: magazines and televisions, so that total exposure is maximized. Each page of magazine advertising is estimated to result in 60,000 exposures, whereas each spot on television is estimated to result in 120,000exposure. Each page of magazine advertising costs birr 9,000 and each spot on television costs birr 12,000. An additional condition that the firm has specified is that at least 2 pages of magazine advertising be used and at least 3 spots on television. Determine the optimal media mix that maximizes the exposure.

6. A furniture workshop makes desks, chairs, and cabinet and bookcases. The work is carried out in three major debarments-designing, Fabrication, and Finishing. Time required per unit of product in hours is:

 Department Desk Chair Cabinet Book Case Time/week Designing 4 2 3 3 800 Fabrication 10 6 8 7 1200 Finishing 10 8 8 8 800

Cost of operation per unit of the products is (birr)

 Department Desk Chair Cabinet Book case Designing 15 8 12 12 Fabrication 30 18 24 21 Finishing 35 28 25 21 Selling price/unit 175 95 145 130

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