A farmer must decide what crops to grow on a 300-hectare tractof land. He can grow oats, wheat, or barley, which yield 50, 100and 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 andbarley, respectively. Government regulations restrict the farmer toa maximum of 150 hectares of wheat and his crop rotation schedulerequires that he plants at least 50 hectares in oats and 50hectares in barley. Because of his storage arrangements, the farmerwants the number of hectares of oats to be equal to or less thanhalf the number of hectares of barley.
a. Formulate algebraically the linear programming model of thisproblem 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 aspreadsheet and SOLVE using Excel solver (Provide a printout of thecorresponding “Excel Spreadsheet” and the “Answer Report”). Include“managerial statements” that communicate the results of theanalyses.
