A farmer has 20 acres to plant in wheat and barley. He has to plant at least 15 acres. Wheat costs $200 per acre to plant and barley costs $150 per acre, and the farmer has only $2400 to spend. If the estimated profit of an acre of wheat is $450 and the estimated profit of an acre of barley is $350, how many acres of each should the farmer plant to maximize his profits?

Question

Tessa Gordon

Mathematics

21 January, 06:09

A farmer has 20 acres to plant in wheat and barley. He has to plant at least 15 acres. Wheat costs $200 per acre to plant and barley costs $150 per acre, and the farmer has only $2400 to spend. If the estimated profit of an acre of wheat is $450 and the estimated profit of an acre of barley is $350, how many acres of each should the farmer plant to maximize his profits?

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Answers (1)

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Claire Decker · Answer 1

16 acres of barley only (no acres of wheat)

Step-by-step explanation:

A graph shows cost of planting puts an upper limit on planted area. The lower limit is provided by the requirement to plant at least 15 acres. The vertices of the feasible solution region are ...

(wheat acres, barley acres) = { (0, 15), (0, 16), (3, 12) }

The profit associated with these scenarios will be ...

for (0, 16) : 16·350 = 5600

for (3, 12) : 3·450 + 12·350 = 1350 + 4200 = 5550

To maximize profit, the farmer should plant 16 acres of barley.