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:

Question

Quizplus · Accepted Answer

The expected price is calculated as (0.25 * $3) + (0.50 * $3.50) + (0.25 * $4) = $3.50. The profit function is P(Q) = (Price * Q) - C(Q). Substituting the expected price and cost function, we get P(Q) = $3.50Q - 0.05Q^2. To maximize profit, take the derivative and set it to zero: dP/dQ = $3.50 - 0.10Q = 0, solving gives Q = 35. Substituting Q = 35 into the profit function gives maximum expected profit = $3.50(35) - 0.05(35)^2 = $122.50.

A Peach Farmer Must Decide How Many Peaches to Harvest