Introduction to Management Science 12th Edition by Bernard Taylor

تمرين 10

Solve the linear programming model formulated in Problem for the Bradley family farm graphically.
a. How many acres of farmland will not be cultivated at the optimal solution Do the Bradleys use the entire 100-acre tobacco allotment
b. What would the profit for corn have to be for the Bradleys to plant only corn
c. If the Bradleys can obtain an additional 100 acres of land, will the number of acres of corn and tobacco they plan to grow change
d. If the Bradleys decide not to cultivate a 50-acre section as part of a crop recovery program, how will it affect their crop plans
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.