Question

9.3. Jean Clark is the manager of the Midtown Saveway Grocery Store. She now needs to replenish her supply of strawberries. Her regular supplier can provide as many cases as she wants. However, because these strawberries already are very ripe, she will need to sell them tomorrow and then discard any that remain unsold. Jean estimates that she will be able to sell 10, 11, 12, or 13 cases tomorrow. She can purchase the strawberries for $3 per case and sell them for $8 per case. Jean now needs to decide how many cases to purchase.

Jean has checked the store’s records on daily sales of strawberries. On this basis, she estimates that the prior probabilities are 0.2, 0.4, 0.3, and 0.1 for being able to sell 10, 11, 12, and 13 cases of strawberries tomorrow.

	Develop a decision analysis formulation of this problem by identifying the decision alternatives, the states of nature, and the payoff table.
	If Jean is dubious about the accuracy of these prior probabilities and so chooses to ignore them and use the maximax criterion, how many cases of strawberries should she purchase?
	How many cases should be purchased if she uses the maximin criterion?

Answer 1

(a)

Decision Alternatives:

Quantity to be purchased (Q) = 10, 11, 12, or 13

States of Nature:

Quantity demanded (D) = 10, 11, 12, or 13

Payoff table:

Q \ D	10	11	12	13
10	$50	$50	$50	$50
11	$47	$55	$55	$55
12	$44	$52	$60	$60
13	$41	$49	$57	$65

Calculations:

(b)

For the Maximax criterion, first, find the maximum payoff for each alternative. Then select the alternative which gives the maximum of these maximums.

So, the best decision is Q=13 as per Maximax rule.

(c)

For the Maximin criterion, first, find the minimum payoff for each alternative. Then select the alternative which gives the maximum of these minimums.

So, the best decision is Q=10 as per Maximin rule.