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)
A) Formulate appropriately as an LP to maximize profit. Provide the algebraic model (similar to the example 3.1 model on slide 15 of chapter 3 PPT) in your submission. Must be neatly presented. (Note: Integer constraints are NOT needed in this problem.)
B) Input and solve the formulation using Excel. After running Solver, generate both the answer report and the sensitivity report.
C) Answer the following questions in the Answer and Sensitivity Report worksheet. Do not modify or rerun the model. You must explain all the steps on how you answered the question based on the output of the one standard LP output which can include Excel’s sensitivity report. 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, explain why this is the case.
I) How much land is planted with wheat?
II) How much land is planted with corn?
III) How much profit will the farm receive from the optimal operation?
IV) What happens to the optimal solution if the profit of wheat doubles? Must explain how you arrived to your answer based on the given output. Do not reformulate the LP to find out the implication.
V) What happens to the optimal solution if the profit of corn decreases by 50%? Must explain how you arrived to your answer based on the given output. Do not reformulate the LP to find out the implication.
VI) What happens to the optimal profit if the farm hires another 100 workers? Must explain how you arrived to your answer based on the given output. Do not reformulate the LP to find out the implication.
VII) What happens to the optimal profit if the farm cuts down 600 tons of fertilizer? Must explain how you arrived to your answer based on the given output. Do not reformulate the LP to find out the implication.
VIII) What happens to the optimal profit if the farm acquires another 30 acres of land? Must explain how you arrived to your answer based on the given output. Do not reformulate the LP to find out the implication.