The produce manager at the local Pig & Whistle grocery store must determine how many pounds of bananas to order weekly. Based on past experience, the demand for bananas is expected to be 100, 150, 200, or 250 pounds with the following probabilities:

- 100 lbs: 0.20
- 150 lbs: 0.25
- 200 lbs: 0.35
- 250 lbs: 0.20

The bananas cost the store $0.45 per pound and are sold for $0.85 per pound. Any unsold bananas at the end of each week are sold to a local zoo for $0.30 per pound.

Use your knowledge of decision analysis to model and solve this problem in order to recommend how many pounds of bananas the manager should order each week.

To model this problem, we can use decision analysis, which involves identifying the possible outcomes, assigning probabilities to each outcome, and calculating the expected value of each decision.

In this case, the possible outcomes are the demand for bananas, which can be 100, 150, 200, or 250 pounds per week. The probabilities of each demand level are given as 0.20, 0.25, 0.35, and 0.20, respectively.

Let X denote the demand for bananas in pounds. Then, the expected demand for bananas, denoted as E(X), can be calculated as follows:

E(X) = 100(0.20) + 150(0.25) + 200(0.35) + 250(0.20) = 182.5

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