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 conditional value for the decision alternative "Stock 3" and state of nature "Sell 1" is
A) 1.4 units.
B) $1 profit.
C) $25 profit.
D) $-8 profit.
E) 25 units.

Question

Quizplus · Accepted Answer

The conditional value for the decision alternative "Stock 3" and state of nature "Sell 1" can be calculated using the formula:

Conditional value = (Probability of state of nature) x (Profit under the decision alternative and state of nature)

For this scenario, the probability of "Sell 1" is 0.3 and the profit under the decision alternative "Stock 3" and state of nature "Sell 1" is calculated as follows:

Profit = (Revenue - Cost) x Units sold
Profit = ($25 - $8) x 1
Profit = $17

Therefore, the conditional value for "Stock 3" and "Sell 1" is:

Conditional value = 0.3 x $17
Conditional value = $5.10

This means that if the retailer stocks 3 units of the product, and the state of nature turns out to be "Sell 1", the expected profit would be $5.10.

Since the conditional value for "Stock 3" and "Sell 1" is positive, it is the best choice for the retailer.

A Retailer Is Deciding How Many of a Certain Product