A farmer owns 450 acres of land. He is going to plant each acre with wheat or corn. Each acre planted with wheat yields $2000 profit, requires three workers, and requires two tons of fertilizer. Each acre planted with corn yields $3000 profit, requires two workers, and requires four tons of fertilizer. There are currently 1000 workers and 1200 tons of fertilizer available.

Define the decision variables necessary for the LP formulation as follows:

X    =    land planted with wheat (acres)

Y    =    land planted with corn (acres)

Formulate appropriately as an LP to maximize profit. Provide the algebraic model

Input and solve the formulation using Excel. After running Solver, generate both the answer report and the sensitivity report.

Answer the following questions in the Answer and Sensitivity Report worksheet. There is no use of SolverTable Add-In with this problem. Just use the standard Solver output. If you feel that it is not possible to answer the question with the single output, please explain why this is the case.

1. What happens to the optimal profit if the farm cuts down 600 tons of fertilizer? Please explain how you arrived to your answer based on the given output.  

2. What happens to the optimal profit if the farm acquires another 30 acres of land? Please explain how you arrived to your answer based on the given output.