Question

A farmer is going to divide her 30 acre farm between two crops. Seed for corn costs $15 per acre. Seed for wheat costs $30 per acre. The farmer can spend at most $750 on seed.If wheat brings in a profit of $110 per acre, and corn brings in a profit of $100 per acre, how many acres of each crop should the farmer plant to maximize her profit

Answer 1

$3200

Explanation:

The total area of land is 30 acre. Let x represent the area in acre that corn is planted and y represent the area in acre that wheat is planted. Therefore:

x + y = 30 (1)

Also, the farmer can spend at most $750 on seeds. Corn cost $15 per acre, maize cost $30 per acre. Hence:

15x + 30y ≤ 750 (2)

Also, x and y > 0

The profit is given by the function:

Profit = 100x + 110y

Graphing equation 1 and equation 2 and solving, we get the points:

(10, 20)

Hence the maximum profit is at:

Max profit = 100(10) + 110(20) = $3200