A farm co-op has 6,000 acres available to plant with corn and soybeans. Each acre of corn requires 9 gallons of fertilizer/herbicide and 0.75 hour of labor to harvest. Each acre of soybeans requires 3 gallons of fertilizer/herbicide and 1hour of labor to harvest. The co-op has available at most 40,508 gallons of fertilizer/herbicide and at most 5,250 hours of labor for harvesting. Find the maximum profit if the profits per acre are $65 for corn and $50 for soybeans. Round your answer to the nearest cent if necessary.
A)$262,500.00
B)$356,270.00
C)$363,365.75
D)$333,730.00
E)$345,000.00

Question

A farm co-op has 6,000 acres available to plant with corn and soybeans. Each acre of corn requires 9 gallons of fertilizer/herbicide and 0.75 hour of labor to harvest. Each acre of soybeans requires 3 gallons of fertilizer/herbicide and 1hour of labor to harvest. The co-op has available at most 40,508 gallons of fertilizer/herbicide and at most 5,250 hours of labor for harvesting. Find the maximum profit if the profits per acre are $65 for corn and $50 for soybeans. Round your answer to the nearest cent if necessary. ​
A)$262,500.00
B)$356,270.00
C)$363,365.75
D)$333,730.00
E)$345,000.00

Quizplus · Accepted Answer

To maximize profit, we need to determine the optimal allocation of acres between corn and soybeans within the constraints of fertilizer/herbicide and labor. Let $x$ be the acres of corn and $y$ be the acres of soybeans. The constraints are:1. $x + y \leq 6000$ (total acres)2. $9x + 3y \leq 40508$ (fertilizer/herbicide)3. $0.75x + y \leq 5250$ (labor)The profit function to maximize is $P = 65x + 50y$.Using linear programming to solve this system of inequalities, we find the optimal allocation of acres to maximize profit. The solution to this problem, given the constraints, yields the maximum profit, which corresponds to choice B, $356,270.00. This involves allocating the resources in such a way that the profit from corn and soybeans is maximized, taking into account the limited availability of fertilizer/herbicide and labor hours.

A Farm Co-Op Has 6,000 Acres Available to Plant with Corn