A farmer has 150 acres of land suitable for cultivating crops A and B. The cost of cultivating crop A is $40/acre and that of crop B is $60/acre. The farmer has a maximum of $7,800 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 3,200 labor-hours available. He has also decided that he will cultivate at least 60 acres of crop A. If he expects to make a profit of $170/acre on crop A and $220/acre on crop B, how many acres of each crop should he plant in order to maximize his profit?
A) The farmer should plant 60 acres of crop A and 80 acres of crop B to realize a maximum profit of $27,800.
B) The farmer should plant 110 acres of crop A and 40 acres of crop B to realize a maximum profit of $27,500.
C) The farmer should plant 60 acres of crop A and 0 acres of crop B to realize a maximum profit of $25,500.

Question

Quizplus · Accepted Answer

The problem can be solved using linear programming. The constraints are the budget ($7,800), labor hours (3,200), and minimum acreage for crop A (60 acres). Maximizing profit leads to the solution of planting 60 acres of crop A and 80 acres of crop B, which fits the constraints and maximizes profit.

A Farmer Has 150 Acres of Land Suitable for Cultivating