A retailer is deciding how many of a certain product to stock. The historical probability distribution of sales for this product is 0 units, 0.2; 1 unit, 0.3; 2 units, 0.4, and 3 units, 0.1. The product costs $8 per unit and sells for $25 per unit. The largest conditional value (profit) in the entire payoff table for this scenario is
A) $-24 profit
B) $-8 profit
C) $17 profit
D) $51 profit
E) $75 profit

Question

Quizplus · Accepted Answer

To find the largest conditional value (profit), we need to multiply the probability of each sales outcome by its corresponding profit and then sum up the results.

The payoff table would look like this:

| Sales | Probability | Revenue | Cost | Profit |
|-------|------------|---------|------|--------|
| 0     | 0.2        | 0       | -8   | -8     |
| 1     | 0.3        | 25      | -8   | 17     |
| 2     | 0.4        | 50      | -16  | 34     |
| 3     | 0.1        | 75      | -24  | 51     |

To find the largest conditional value, we need to look at the highest profit value, which is $51 for selling 3 units. Therefore, the best choice is to stock 3 units.

A Retailer Is Deciding How Many of a Certain Product