Question

A peach farmer must decide how many peaches to harvest for the world peach fair. He knows that there is a 25 percent chance that the world price will be $3, a 50 percent chance that it will be $3.50, and a 25 percent chance that it will be $4. His cost function is C(Q) = 0.05Q2. The farmer's maximum expected profit is:
a. $61.25.
b. 0.
c. $122.50.
d. None of the answers are correct.

Answer 1

Answer:

The correct option is a. $61.25.

Explanation:

Note: The correct cost function of the farmer is as follows:

C(Q) = 0.05Q^2 ……………….. (1)

Differentiating equation

MC = C’(Q) = 0.1Q

P = Expected price = (25% * $3) + (50% * $3.50) + (25% * $4) = $3.50 ……. (2)

Since profit is maximized when MC = P, we equate equations (1) and solve for Q which is the expected profit-maximizing quantity as follows:

0.1Q = 3.50

Q = 3.50 / 0.1 = 35

Substituting Q = 35 into equation (1), we have:

C(Q) = 0.05 * 35^2 = $61.25

R(Q) = Maximum expected revenue = P * Q = $3.50 * 350 = $122.50

The farmer's maximum expected profit = R(Q) - C(Q) = $122.50 - $61.25 = $61.25

Therefore, the correct option is a. $61.25.