Question

A farmer owns a 2000-acre farm and can plant any combination of two crops, A and B. Crop A requires 1 person-day of labor and $90.00 of capital for each acre planted, while crop B requires 2 person-days and $60.00 of capital for each acre planted. Crop A produces $170.00 in revenue per acre, and crop B produces $190.00 in revenue per acre. The farmer has $150,000.00 of capital and 3000 person-days of labor available for the year. How many acres of each crop should the farmer plant in order to maximize the total revenue?

Answer 1

A+2b=3000
90a+60b=150000

-90a-180b=-127000
90a+60b=150000

-120b=-120000
b=1000

a+2000=3000
a=1000

crop a=1000
crop b=1000