Question

Small farm has 70 acres of space to plant.farmer wants to grow corn and green beans. cost $60/acre to grow corn and $30 acre for green beans. Farmer has $1800 to use. Takes farmer 3 days to plant acre of corn and 4days to plant acre of green beans. 120 days available to plant vegetables. Farmer's profit is $180/acre of corn and $100/acre of green beans. How many acres should farmer allow for each vegetable to maximize profit?

Answer 1

Let c=acres of corn planted and b=acres of beans planted. The farm has 70 acres altogether so\[b+c=70\]The farmer has $1800 to use to plant so the amount it costs to plant should be\[30b+60c \le1800\] The farmer has 120 days available for planting so\[4b+3c \le120\]Finally the farmer wants to maximize profit\[\max P=100b+180c\]