Question

A farmer's tomato crop is wilting, and he must decide whether to water it. If he waters the tomatoes, or if it rains, the crop will yield $1,000 in profits; but if the tomatoes get no water they will yield only $500. Operation of the farmer's irrigation system costs $100. The farmer seeks to maximize expected profits from tomato sales. If the farmer believes there is a 50 percent chance of rain, should he water?

Answer 1

The farmer should water the tomatoes since the expected profit of watering ($900) exceeds the expected profit of not watering ($750), making watering the crop the profit-maximizing decision.

Step-by-step explanation:

The farmer's decision on whether to water the tomatoes should be based on the expected value of each scenario. With a 50 percent chance of rain, the expected profit from not watering is calculated as (0.5 × $1000) + (0.5 × $500) = $750. On the other hand, watering the tomatoes guarantees $1000, minus the $100 watering cost, resulting in a profit of $900. Therefore, the expected profits are higher if the farmer waters the crop.

The farmer should compare the expected profits of each option. Here, watering has an expected profit of $900, whereas not watering has an expected profit of only $750. Since $900 is greater than $750, the profit maximizing decision would be to water the tomatoes, ensuring the highest expected profits.