A farmer owns 450 acres of land. He is going to plant each acre with wheat or corn. Each acre planted with wheat yields 2,000 pounds of wheat, requires three workers, and two tons of fertilizer. Each acre planted with corn yields 3,000 pounds of corn, requires two workers, and four tons of fertilizer. The wheat can be sold at the selling price of $2.5 per pound, whereas the corn at the price of $3.4 per pound. To pay for the workers and the fertilizers it is estimated that the farmer will have to incur a cost of $0.5 per pound of wheat and of $0.4 per pound of corn. There are currently 1,000 workers and 1,200 tons of fertilizer available.
a) Create a model in Excel and use Solver to help the farmer maximize the profit from his land.
b) Generate the sensitivity report from Solver. Imagine you can change the selling price for a pound of wheat, while all the other parameters remain the same. What is the minimum selling price per pound of wheat that would make it optimal to produce wheat? Explain your reasoning.
c) What amount of extra profits will the company make if it has extra 100 tons of fertilizers available? Explain your reasoning.
d) Suppose the farmer has the possibility to acquire additional 50 acres of land to increase the production. What amount of extra profits will the farmer attain with this extra land?
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