Question

A farmer is going to divide her 50-acre farm between two crops. Seed for crop A costs $25 per acre. Seed for crop B costs $50 per acre. The farmer can spend at most $1750 on

Answer 1

The farmer should allocate 30 acres to crop A and 20 acres to crop B to maximize the crop yield given the budget constraint.

Step-by-step explanation:

This is a problem involving 2 variables and a budget constraint. Let's denote the number of acres allocated to crop A as x, and the number of acres allocated to crop B as y. The budget constraint is given by: 25x + 50y ≤ 1750. We also know that x + y = 50, as the total number of acres on the farm is 50 acres. To solve this problem, we can use either substitution or elimination method. Let's use substitution method:

First, let's solve the second equation for x: x = 50 - y.

Now, substitute this value of x into the first equation:

25(50 - y) + 50y ≤ 1750.

Simplify the equation:

1250 - 25y + 50y ≤ 1750.

Combine like terms:

25y ≤ 500.

Divide both sides by 25:

y ≤ 20.

So, the number of acres allocated to crop B should be less than or equal to 20 acres.

Now, substitute this value of y back into the equation x + y = 50:

x + 20 = 50.

Solve for x:

x = 30.

So, the number of acres allocated to crop A should be 30 acres.

Therefore, the farmer should allocate 30 acres to crop A and 20 acres to crop B to maximize the crop yield given the budget constraint.