Problems:
A farmer has a 40-acre farm in Georgia. The farmer is using linear programming to determine how many acres of corn, peanuts, and cotton to plant. Each crop requires labor, fertilizer, and insecticide, and the farmer has formulated the linear programming model below, and solved it in excel solver, with the results and sensitivity report given below. Note that the model is a profit maximization problem. The farmer has estimates of revenue per acre for the three crops, and has estimated the cost per acre for each crop, where the costs included are, among other things, the labor, fertilizer, and insecticide costs. Using the revenue and cost estimates, he or she has calculated the profit per acre for each crop. The farmer owns the land and considers that a fixed cost, not a variable cost, so that the cost of land is not included in the profit calculations, but the costs of labor, fertilizer, and insecticide are included.
Please consider each question below separate and independent of all other questions here. Each question is in reference to the original problem and its solution and sensitivity report, given on the previous page. Answer each question using only information available in the solution and sensitivity report given, and not based on any subsequent solver that you may make. Do not attempt to resolve the problem to answer these questions.
a. How many acres of each crop should the farmer plant and what it the total profit?
b. How much labor, fertilizer, insecticide, and land does this solution use?
c. There is speculation that the profit on corn may go up due to an increase in its revenue. If the profit per acre goes to $500, would the solution change? Would total profit change? Why or why not?
d. If the profit per acre on peanuts drops to $300, would the solution change? Why or why not?
e. Suppose that the farmer buys an additional 10 tons of insecticide at its original cost and resolves the problem. Would the solution change? Would the total profit change? If so, can you, using only the original sensitivity report, determine the new profit? If so, what is the new total profit?
f. Suppose that the farmer is offered 10 tons of insecticide for $100 per ton; should he or she or she buy it? Why or why not?
g. If the profit for all three crops increases by $10 per acre, does the solution change? Please show work to support your answer.
h. If available labor decreases by 5 hours, and available fertilizer and insecticide each decrease by 5 tons, and available land decreases by 1 acre, does the solution change? Does the total profit change? If so, can you, using only the original sensitivity report, determine the new profit? If so, what is the new total profit? Please show work to support your answer.