A retailer is deciding how many units 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 $10 per unit and sells for $33 per unit. What is the smallest conditional value (profit) in the entire payoff table for this scenario?
A) $-30 profit
B) $3 profit
C) $36 profit
D) $66 profit
E) $75 profit

Question

Quizplus · Accepted Answer

To find the smallest conditional value (profit), we need to calculate the profit for each possible sales outcome and then multiply it by the probability of that outcome. The payoff table would look like this:

| Units sold | Probability | Revenue | Cost | Profit |
|------------|-------------|---------|------|--------|
| 0          | 0.2         | $0      | $0   | $0     |
| 1          | 0.3         | $33     | $10  | $23    |
| 2          | 0.4         | $66     | $20  | $46    |
| 3          | 0.1         | $99     | $30  | $69    |

To find the smallest conditional value, we need to find the minimum value of (Profit*Probability) in the table. The smallest value is -$6, which occurs when 0 units are sold. This means that the retailer loses the cost of stocking the product, which is $10 per unit. Therefore, the smallest conditional value (profit) is -$10*0.2= -$2, and the smallest overall profit is -$6. The closest answer choice to this is A, which is $-30 profit.

A Retailer Is Deciding How Many Units of a Certain