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A farmer in Fayetteville owns 50 acres of land. He is going to plant each acre with cotton or corn. Each acre planted with cotton yields $400 profit; each with corn yields $200 profit. The labor and fertilizer used for each acre are given in the table below. Resources available include 150 workers and 200 tons of fertilizer.
Cotton Corn Labor (Workers)
5
3
Fertilizer (Tons)
6
2
(A) Formulate a linear programming model that will enable the farmer to determine the number of acres that should be planted cotton and/or corn in order to maximize his profit.
(B) Find an optimal solution to the model in (A) and determine the maximum profit.
(C) Implement the model in (A) in Excel Solver and obtain an answer report. Which constraints are binding on the optimal solution?
(D) Obtain a sensitivity report for the model in (A). How much should the farmer be willing to pay for an additional worker?
(E) Suppose the farmer hires 10 additional workers. Can you use the sensitivity analysis obtained for (D) to determine his expected profit? Would his planting plan change? Explain your answer.
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