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 200 acres may be planted in soybeans. During the planting season 1200 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.
a. Formulate the problem as a linear program.
b. Solve using the corner-point method.
Let X1 = number of acres of soybeans to plant
Let X1 = number of acres of sugar cane to plant
Maximize profit = 1000X1 + 2000X2
Subject to
X1 ≤ 200
2X1 + 5X2 ≤ 1200
X1 + X2 ≤ 500
X1, X2 ≥ 0
The optimal solution is 200 acres in soybeans and 160 acres in sugar cane. There's not enough labor to plant all 500 acres when 200 acres are in soybeans.
Corner Points
X1 X2 Z
0 0 0.
200 0 200,000.
0 240 480,000.
200 160 520,000.
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