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 optimal solution?
A) 300 acres of soybeans, 180 acres of sugar cane
B) 300 acres of soybeans, 200 acres of sugar cane
C) 0 acres of soybeans, 300 acres of sugar cane
D) 500 acres of soybeans, 0 acres of sugar cane
E) 300 acres of soybeans, 100 acres of sugar cane

Question

Quizplus · Accepted Answer

The optimal solution maximizes profit while adhering to the constraints: no more than 300 acres of soybeans, a total of 500 acres of land, and 1500 hours of planting time. Planting 300 acres of soybeans uses 600 hours (300 acres * 2 hours/acre), leaving 900 hours for sugar cane. At 5 hours per acre for sugar cane, this allows for 180 acres (900 hours / 5 hours/acre). This combination uses all available land (300 + 180 = 480 acres) and planting time, maximizing profit within the given constraints.

Rienzi Farms Grows Sugar Cane and Soybeans on Its 500