Question

A farmer is going to divide her 40 acre farm between two crops. Seed for crop A costs $15 per acre. Seed for crop B costs $30 per acre. The farmer can spend at most $900 on seed. If crop B brings in a profit of $50 per acre, and crop A brings in a profit of $110 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

The answer is below

Explanation:

Let x represent the number of acre on which crop A is farmed and B represent the number of acre crop B is farmed.

Therefore:

Since there is a total of 40 acre farm, hence:

x + y = 40 (1)

The farmer can spend at most $900 on seed, crop A seed cost $15 and crop B seed cost $50, hence:

15x + 50y ≤ 900 (2)

Her profit is given as:

Profit = 50x + 110y

From the geogebra plot, the point that maximizes the profit is at (60, 0)

Therefore the maximum profit = 50(60) + 110(0) = $3000