A farmer has a field of 70 acres in which he plants potatoes and corn. Continued below...

Question

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.

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What are the constraints for the problem?

What is the profit equation?

What is the optimal solution?

Answer 1

Profit equation = 150p + 50c - 20p - 60c or 130p-10c where p is number of acres of potato sold and c is the number of acres of corn sold

Optimal solution is when 130p > 10c or p > 13

Constraint is the acres he has available so p + c <= 70

20p + 60c <= 3000

p >= 0

c >= 0

maximize the profit equation. 150p + 50c make all potato crops and no corn