Consider the linear programming problem

A farmer has a field of 70 acres in which he plants potatoes and corn. The seed for potatoes costs $20/acre, the seed for corn costs $60/acre, and the farmer has set aside $3000 to spend on seed. The profit per acre of potatoes is $150 and the profit for corn is $50 an acre. How many acres of each should the farmer plant?

acres of potatoes

acres of corn

What is the maximum profit? $

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  1. maximize
    150 x + 50 y

    x + y <=70

    20 x + 60 y <= 3000

    x>= 0
    y>= 0
    x+y >=1 to fill in input form only

    result 10500 at (70,0)

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  2. which we could have seen without doing the problem :) The potato seed costs less and the profit is more

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  3. Thanks!

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  4. You are welcome.

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