The Bradley family owns 410 acres offarmland in North Carolina on which they grow corn and tobacco.Each acre of corn costs $105 to plant, cultivate, and harvest; eachacre of tobacco costs $210. The Bradleys’ have a budget of $52,500for next year. The government limits the number of acres of tobaccothat can be planted to 100. The profit from each acre of corn is$300; the profit from each acre of tobacco is $520. The Bradleys’want to know how many acres of each crop to plant in order tomaximize their profit.
a. Formulate the linear programmingmodel for the problem and solve.
b. How many acres of farmland will notbe cultivated at the optimal solution? Do the Bradleys use theentire 100-acre tobacco allotment?
c. The Bradleys’ have an opportunityto lease some extra land from a neighbor. The neighbor is offeringthe land to them for $110 per acre. Should the Bradleys’ lease theland at that price? What is the maximum price the Bradleys’ shouldpay their neighbor for the land, and how much land should theylease at that price?
d. The Bradleys’ are consideringtaking out a loan to increase their budget. For each dollar theyborrow, how much additional profit would they make? If theyborrowed an additional $1,000, would the number of acres of cornand tobacco they plant change?
