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Maximum profit

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A farmer grows two crops, corn and soybeans. Suppose that each acre planted with corn requires 1 man day of labor, $3 investment and yields a profit of $35 at harvest. Each acre of soybeans on the other hand requires 2 man days of labor,$1 investment and returns a profit of $20 at harvest. The farmer had a total of 70 acres available for these crops. He has $140 he can invest and 80 man days of labor available. How many acres of each crop should he plant for maximum profit?

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Solution Summary

This shows how to find maximum profit for a farmer planting crops.

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Let, on X acres of earth Corn is planted, and on Y acres Soybean is planted.

labor constrain:
1*X + 2*Y <= 80
=> X + 2Y <= 80 ...(1)

Field constrain:
X+Y = 70 ........(2)

Profit:
P(X,Y) = (35-3)*X + (20-1)*Y
=>P(X,Y) = 32X + 19Y ..(3)

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Solution provided by:
Amrit Lal Ahuja, PhD (IP)
Education
  • BEng, Allahabad University, India
  • MSc , Pune University, India
  • PhD (IP), Pune University, India
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