# Maximum profit

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 Preview

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)

Take ...

#### Solution Summary

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