Introduction to Management Science 12th Edition by Bernard Taylor

Exercise 14

Solve the linear programming model formulated in Problem for the Bradley farm by using the computer.
a. The Bradleys have an opportunity to lease some extra land from a neighbor. The neighbor is offering the land to them for $110 per acre. Should the Bradleys lease the land at that price What is the maximum price the Bradleys should pay their neighbor for the land, and how much land should they lease at that price
b. The Bradleys are considering taking out a loan to increase their budget. For each dollar they borrow, how much additional profit would they make If they borrowed an additional $1,000, would the number of acres of corn and tobacco they plant change
Problem
The Bradley family owns 410 acres of farmland in North Carolina on which they grow corn and tobacco. Each acre of corn costs $105 to plant, cultivate, and harvest; each acre of tobacco costs $210. The Bradleys have a budget of $52,500 for next year. The government limits the number of acres of tobacco that 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 to maximize their profit.
Formulate a linear programming model for this problem.