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 $8 per unit and sells for $25 per unit.What is the conditional value for the decision alternative "Stock 3" and state of nature "Sell 1"?
A)1.4 units
B)$1 profit
C)$25 profit
D)$-8 profit
E)$23.80 profit

Question

Quizplus · Accepted Answer

The conditional value for the decision alternative "Stock 3" and state of nature "Sell 1" can be calculated as follows:
Conditional Value = (Probability of selling 1 unit given that 3 units are stocked) x (Profit from stocking 3 units)
Probability of selling 1 unit given that 3 units are stocked = 0.1 (from the probability distribution)
Profit from stocking 3 units = (Revenue from selling 1 unit - Cost of stocking 3 units) = ($25 - $8x3) = $1
Therefore, Conditional Value = 0.1 x $1 = $0.10
Since the conditional value is positive, stocking 3 units is a profitable decision. However, it is not the best choice as there may be other decision alternatives with higher conditional values.

A Retailer Is Deciding How Many Units of a Certain