Problem I (20 points). Consider a farmer who has a total of 500 acres of land available for growing crops A, B and C. The planting costs per acre are $150, $230, and $260 for A, B and C respectively. The farmer needs at least 200 tons (T) of A and 240 T of B for the cattle feed which can be grown on the farm or bought from a wholesaler. The purchase prices of A resp. B per ton are $238 for A and $210 for B. The amount of A and B produced in excess will be sold at prices of $170 per ton for A and $150 per ton for B. For crop C, there is a quota on production which is 6000 T for the farmer. Any amount of crop C up to the quota can be sold at $36 per ton, the amount in excess of the quota is limited to 10 per ton. 1. The farmer would like to determine the optimal amount of each crop to be produced or purchased from whole seller and sold so as to maximize the profit. Please formulate the mathematical model specifying the triple (S,Q,M) and the un- known quantities making the necessary assumptions where ever needed. For example, the amount of a crop produced equals the acres of land devoted to a crop. 2. Write a Maxima code to solve the resulting linear programming problem. Please name your code lastname.p1.mac. Commit this to your repository under the folder home- work_01. Problem I (20 points). Consider a farmer who has a total of 500 acres of land available for growing crops A, B and C. The planting costs per acre are $150, $230, and $260 for A, B and C respectively. The farmer needs at least 200 tons (T) of A and 240 T of B for the cattle feed which can be grown on the farm or bought from a wholesaler. The purchase prices of A resp. B per ton are $238 for A and $210 for B. The amount of A and B produced in excess will be sold at prices of $170 per ton for A and $150 per ton for B. For crop C, there is a quota on production which is 6000 T for the farmer. Any amount of crop C up to the quota can be sold at $36 per ton, the amount in excess of the quota is limited to 10 per ton. 1. The farmer would like to determine the optimal amount of each crop to be produced or purchased from whole seller and sold so as to maximize the profit. Please formulate the mathematical model specifying the triple (S,Q,M) and the un- known quantities making the necessary assumptions where ever needed. For example, the amount of a crop produced equals the acres of land devoted to a crop. 2. Write a Maxima code to solve the resulting linear programming problem. Please name your code lastname.p1.mac. Commit this to your repository under the folder home- work_01
