A farmer in Iowa owns 45 acres of land. He is going to plant each acre with wheat or corn. Each acre planted with wheat yields $200 profit, requires 3 workers, and requires 2 tons of fertilizer; each with corn yields $300 profit, requires 2 workers, and requires 4 tons of fertilizer.

The farmer has 100 workers and 120 tons of fertilizer available.

a. Use Solver to help the farmer maximize the profit from his land.

b. Confirm graphically that the solution from part a maximizes the farmer’s profit from his land.

c. Starting with the optimal solution, use SolverTable to see what happens to the decision variables and the total profit when the availability of fertilizer varies from 20 tons to 220 tons in 10-ton increments.

When does the farmer discontinue producing wheat? When does he discontinue producing corn? How does the profit change for each 10-ton increment? Make this more obvious by creating a line chart of profit (vertical axis) versus fertilizer availability.