A farmer plans to grow wheat and corn. Each acre of wheat requires 4 hours of labor and $20 of capital, and each acre of corn requires 16 hours of labor and $40 of capital. The farmer has at most 800 hours of labor and $2400 of capital available. If the profit from an acre of wheat is $80 and from an acre of corn is $100, how many acres of each crop should she plant to maximize her profit?

To maximize profits, the farmer should plant 120 acres of wheat, and no acre of corn.

Step-by-step explanation:

Given that a farmer plans to grow wheat and corn, and each acre of wheat requires 4 hours of labor and $ 20 of capital, and each acre of corn requires 16 hours of labor and $ 40 of capital, and the farmer has at most 800 hours of labor and $ 2400 of capital available, if the profit from an acre of wheat is $ 80 and from an acre of corn is $ 100, to determine how many acres of each crop should she plant to maximize her profit the following calculation must be performed:

Knowing that each acre of wheat has a 50% lower capital cost, 75% lower hours and a 20% lower profit, in principle this would be the crop to be planted to obtain better yields.

2400/20 = 120

120 x 4 = 480

120 x 80 = 9,600

Thus, to maximize profits, the farmer should plant 120 acres of wheat, and no acre of corn.