Question

A farmer is going to divide her 50 acre farm between two crops. Seed for crop A costs $10 per acre. Seed for crop B costs $5 per acre. The farmer can spend at most $400 on seed. If crop B brings in a profit of $90 per acre, and crop A brings in a profit of $120 per acre, how many acres of each crop should the farmer plant to maximize her profit?
acres of crop A
acres of crop B

Answer 1

Answer:

To maximize the profit, the farmer should plant 30 acres of crop A and 20 acres of crop B

Step-by-step explanation:

Let

x -----> the number of acres of crop A

50-x ----> the number of acres of crop B

we know that

$10x+5(50-x) \leq 400$

$10x+250-5x \leq 400$

$10x-5x \leq 400-250$

$5x \leq 150$

$x \leq 30$ ----> inequality A

The maximum value of x is 30 acres

The profit is equal to

$P=120x+90(50-x)$

For x=30

Find the value of P

$P=120(30)+90(50-30)$

$P=120(30)+90(20)$

$P=\ 5,400$

therefore

To maximize the profit, the farmer should plant 30 acres of crop A and 20 acres of crop B