Chapter 12.1, Problem 9E

Decision Making Based on Expected Value A citrus grower anticipates a profit of $\$100,000$ this year if the nightly temperatures remain mild. Unfortunately, the weather forecast indicates a $25\%$ chance that the temperatures will drop below freezing during the next week. Such freezing weather will destroy $40\%$ of the crop and reduce the profit to $\$60,000$. However, the grower can protect the citrus fruit against the possible freezing (using smudge pots, electric fans, and so on) at a cost of $\$5000$. Should the grower spend the $\$5000$ and thereby reduce the profit to $\$95,000$? [Hint: Compute $\text{E}\left(X\right)$ where $X$ is the grower will get if he does nothing to protect the fruit.]