Farmer Jones's Planting Problem
Farmer Jones must determine how many acres of corn and how many acres of wheat to plant this year to maximize his revenues. An acre of wheat yields 25 bushels of wheat and requires 10 hours of labor per week. An acre of corn yields 10 bushels of corn and requires 4 hours of labor per week. All wheat can be sold at $4 a bushel, and all corn can be sold at $3 a bushel. Seven acres of land and 40 hours per week of labor are available. Government regulations require that at least 30 bushels of corn be produced during the current year.
a) Mathematically formulate a linear programming model for this problem. Define decision variables, and then define your constraints and objective function accordingly. Combine everything to get the final model.
b) Formulate and solve this problem on a spreadsheet using Excel.