A farmer has 150 acres of land suitable for cultivating crops A and B. The cost of cultivating crop A is $40/acre, whereas that of crop B is $60/acre. The farmer has a maximum of $7,400 available for land cultivation. Each acre of crop A requires 20 labor-hours, and each acre of crop B requires 25 labor-hours. The farmer has a maximum of 3,300 labor-hours available. If he expects to make a profit of $150/acre on crop A and $200/acre on crop B, how many acres of each crop should he plant in order to maximize his profit? What is the largest profit the farmer can realize? Are there any resources left over?
A) 65 acres of crop A, 80 acres of crop B; maximum profit $25750; $0 left over, 5 acres of land left over, 0 labor-hours left over
B) 150 acres of crop A, 80 acres of crop B; maximum profit $51,000; $2,200 left over, 0 acres of land left over, 0 labor-hours left over
C) 90 acres of crop A, 60 acres of crop B; maximum profit $51,000; $200 left over, 0 acres of land left over, 0 labor-hours left over
D) 150 acres of crop A, 0 acres of crop B; maximum profit $22,500; $2,200 left over, 0 acres of land left over, 300 labor-hours left over

Question

Quizplus · Accepted Answer

This problem can be solved using linear programming. The constraints are the budget ($7,400), the labor hours (3,300), and the land (150 acres). By setting up the equations for these constraints and the profit function (150A + 200B), and solving for maximum profit, option A yields the highest profit without exceeding any resource constraints.

A Farmer Has 150 Acres of Land Suitable for Cultivating