Question

A farmer is going to divide her 50 acre farm between two crops. Seed for crop A costs $50 per acre. Seed for crop B costs $25 per acre. The farmer can spend at most $2,250 on seed. If crop B brings in a profit of $90 per acre, and crop A brings in a profit of $220 per acre, how many acres of each crop should the farmer plant to maximize her profit? Write the objective function then use the feasible region shown in the graph below to maximize it.

Let x = the number of acres of crop A

Let y = the number of acres of crop B

Answer 1

cost: 50x+25y
profit: 220x + 90y
So, you want to
maximize p = 220x+90y subject to:
50x+25y <= 2250
0 <= x
0 <= y
x+y = 50
So, draw the region and evaluate p(x,y) on the vertices of the boundary.