The Smith family owns 405 acres of farmland in Virginia on which they grow corn and tobacco. Each acre of corn costs $110 to plan, cultivate, and harvest; each acre of tobacco costs $215. The Smith family budget $55,000 for next year. The government wants to limit the number of acres of tobacco that can be planted to 100 acres. The profit for each acre of corn is $325; the profit from ecah acre of tobacco is $525. How many acres of each acre of each crop should be planted in order to maximize profit?
a. Formulate a linear programming model and solve.
b. How many acres of farmland will not be cultivated at the optimal solution? Do the Collins use the entire 100 acre allotment?
c. What would the profit for corn have to be for the Collins to plant only corn?
d. If the Collins can obtain an additional 100 acres of land, will the number of acres of corn and tobacco they plan to grow change?
e. If they decide not to cultivate a 50 acre section as part of a crop-recovery program, how will it affect their crop plans?