Rienzi Farms grows sugar cane and soybeans on its 500 acres of land. An acre of soybeans brings a $1000 contribution to overhead and profit; an acre of sugar cane has a contribution of $2000. Because of a government program no more than 300 acres may be planted in soybeans. During the planting season 1500 hours of planting time will be available. Each acre of soybeans requires 2 hours, while each acre of sugar cane requires 5 hours. The company seeks maximum contribution (profit) from its planting decision. What is the maximum profit?
A) $1,000,000
B) $700,000
C) $660,000
D) $600,000
E) $300,000

Question

Quizplus · Accepted Answer

To maximize contribution, we need to find the optimal mix of soybeans and sugar cane that maximizes the contribution. Let x be the number of acres of soybeans and y be the number of acres of sugar cane. We have two constraints:
x + y ≤ 500 (total land available)
2x + 5y ≤ 1500 (total planting time available)
And one additional constraint that limits the soybean acreage:
x ≤ 300
The objective function (contribution) is:
Contribution = 1000x + 2000y
Using linear programming, we can solve this problem and find that the maximum contribution occurs at x = 300 and y = 200. Therefore, the maximum contribution (profit) is:
1000(300) + 2000(200) = $660,000. 
Thus, the answer is C) $660,000.

Rienzi Farms Grows Sugar Cane and Soybeans on Its 500