A farmer owns 450 acres of land. He is going to plant each acre with wheat or corn. Each acre planted with wheat yields $4000 profit, requires three workers, and requires two tons of fertilizer. Each acre planted with corn yields $2000 profit, requires two workers, and requires four tons of fertilizer. There are currently 1000 workers and 1200 tons of fertilizer available. To hedge against risk, the farmer wants to sure that the acres of wheat do not exceed the acres of corn by 150 acres; similarly, the farmer wants to sure that the acres of corn do not exceed the acres of wheat by 150 acres.

Let’s define the decision variables as follows:

W: acres of wheat; C: acres of corn

1. Please formulate the objective function of this farmer.

2. Please write down all the constraints of this LP problem.

3. Please create a coordinate plane, putting W on the horizontal axis and C on the vertical axis.

4. Plot all boundary lines.

5. Identify feasible region.

6. Compute the coordinates and the objective value for each corner of the feasible region.

7. Clearly state your optimal solution and optimal objective value.