A farmer plans to plant two crops, A and B. The cost of cultivating crop A is $40/acre and the cost of cultivating crop B is $60/acre. The farmer has a maximum of $7400 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 3300 labor hours available. If they expect to make a profit of $150/acre on crop A and $200/acre on crop B, how many acres of each crop should they plant to maximize profit? What is the optimal profit?
A farmer plans to plant two crops, A and B. The cost of cultivating crop A is $40/acre and the cost of cultivating crop B is $60/acre. The farmer has a maximum of $7400 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 3300 labor hours available. If they expect to make a profit of $150/acre on crop A and $200/acre on crop B, how many acres of each crop should they plant to maximize profit? What is the optimal profit?
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.CM: Cumulative Review Problem Set
Problem 115CM
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A farmer plans to plant two crops, A and B. The cost of cultivating crop A is $40/acre and the cost of cultivating crop B is $60/acre. The farmer has a maximum of $7400 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 3300 labor hours available. If they expect to make a profit of $150/acre on crop A and $200/acre on crop B, how many acres of each crop should they plant to maximize profit? What is the optimal profit?
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