A farmer grows wheat and corn on a 45 acre farm. He can asell at most 140 bushels of wheat and 120 busheld of corn. Each acre planted with wheat yields 5 bushels, and each acre planted with corn yields 4 bushels. Wheat sells for $30 a busjel and corn sells for $50 a bushel.
To harvest an acre of wheat required 6 hours of labor; 10 hours are needed to harvest an acre of corn. Up to 350 hours of labor can be purchased at $10/hour. Formulate an LP to maximize the farmers profit.
1.) Clearly define the decision variables.
2.) formulate the appropriate Linear Programming model.
3.) Solve the LP model. Use Lingo or other SW
4.) What is the optimal solution
5.) what is the profit associated with the optimal solution.
6.) are they multiple optimal solutions? WHat is one alternative.
7.) What will be the profit if there were only 40 acres
8.) what will be the profit if the proce of wheat droped to $26