Question

A farmer can plant a combination of two different crops on 20 acres of land. Seed costs $120 per acre for crop A and $200 per acre for crop B. Government restrictions limit acreage of crop A to 15 acres, but do not limit crop B. Crop A will take 15 hours of labor per acre at a cost of $5.60 per hur, and crpo B will require 10 hours of labor per acre at $5.00per hour. IF the expected income from crop A is $600 per acre and from crop B is $520 per acre, how many acres of crop A should be planted in order to maximize profit?

Please help me set this up. I am no good with word problems!

Thanks

Answer 1

acres of A = a
acres of B = b
Profit from A = 600a -120a -15(5.60)a
=396a
Profit from b = 520b - 200 b -10(5.00)b
=270b
Well, we want to plant as much A as possible so 15 acres of a and only 5 of b