Question

A farmer must decide what crops to grow on a 300-hectare tract of land. He can grow oats, wheat, or barley, which yield 50, 100 and 80 kg/hectare (respectively) and sell for $1.00, $0.80, and $0.60 per kg (respectively). Production costs (fertilizer, labor, etc.) are $40, $50, and $40 per hectare for growing oats, wheat and barley, respectively. Government regulations restrict the farmer to a maximum of 150 hectares of wheat and his crop rotation schedule requires that he plants at least 50 hectares in oats and 50 hectares in barley. Because of his storage arrangements, the farmer wants the number of hectares of oats to be equal to or less than half the number of hectares of barley.

a. Formulate algebraically the linear programming model of this problem that will maximize the farmer profit (i.e. revenue – cost) and help him/her decides what crops to grow on his/her land (i.e. define the decision variables, objective function, constraints).

b. Formulate this same linear programming problem on a spreadsheet and SOLVE using Excel solver (Provide a printout of the corresponding “Excel Spreadsheet” and the “Answer Report”). Include “managerial statements” that communicate the results of the analyses.

Answer 1

1. Formulate the problem in the excel as shown below.

2. Take note of the formulas

3. Update the solver inputs

4. Output

5.Other outputs