What is the souvenir retailer maximax decision

Assignment Help Applied Statistics

Reference no: EM132277043

Homework Problems: Exercises

Exercise 1 - Debbie Gibson is considering three investment options for a small inheritance that she has just received-stocks, bonds, and money market. The return on her investment will depend on the performance of the economy, which can be strong, average, or weak. The returns for each possible combination are shown in the following table:

INVESTMENT	STRONG	AVERAGE	WEAK
Stocks	12%	6%	-10%
Bonds	7%	4%	1%
Money market	4%	3%	2%

Assume that Debbie will choose only one of the investment options.

(a) Which investment should Debbie choose if she uses the maximax criterion?

(b) Which investment should Debbie choose if she uses the maximin criterion?

(d) Which investment should Debbie choose if she uses the criterion of realism with α = 0.5?

(e) Which investment should Debbie choose if she uses the minimax regret criterion?

Exercise 2 - Waldo Books needs to decide how many copies of a new hardcover release to purchase for its shelves. The store has assumed that demand will be 50, 100, 150, or 200 copies next month, and it needs to decide whether to order 50, 100, 150, or 200 books for this period. Each book costs Waldo $20 and can be sold for $30. Waldo can sell any unsold books back to the supplier for $4.

(a) Which option should Waldo choose if it uses the maximax criterion?

(b) Which option should Waldo choose if it uses the maximin criterion?

(d) Which option should Waldo choose if it uses the criterion of realism with α = 0.7?

(e) Which option should Waldo choose if it uses the minimax regret criterion?

Exercise 3 - A souvenir retailer has an opportunity to establish a new location inside a large airport. The annual returns will depend primarily on the size of the space she rents and if the economy will be favorable. The retailer has worked with the airport concession commission, and has projected the following possible annual earnings associated with renting a small, medium, large, or very large space:

SIZE	GOOD ECONOMY	FAIR ECONOMY	POOR ECONOMY
Small	$70,000	$28,000	-$14,000
Medium	$112,000	$42,000	-$28,000
Large	$140,000	$42,000	-$56,000
Very Large	$420,000	$35,000	-$224,000

(a) What is the souvenir retailer's maximax decision?

(b) What is her maximin decision?

(d) What is her criterion of realism decision, using α = 0.8?

(e) What is her minimax regret decision?

Exercise 4 - A group of medical professionals is considering constructing a private clinic. If patient demand for the clinic is high, the physicians could realize a net profit of $100,000. If the demand is low, they could lose $40,000. Of course, they don't have to proceed at all, in which case there is no cost. In the absence of any market data, the best the physicians can guess is that there is a 50-50 chance that demand will be good.

(a) Construct a decision tree to help analyze this problem. What should the medical professionals do?

(b) The physicians have been approached by a market research firm that offers to perform a study of the market at a fee of $5,000. The market researchers claim that their experience enables them to use Bayes' theorem to make the following statements of probability:

probability of high demand given a positive study result = 0.82
probability of low demand given a positive study result = 0.18
probability of high demand given a negative study result = 0.11
probability of low demand given a negative study result = 0.89
probability of a positive study result = 0.55
probability of a negative study result = 0.45

Expand the decision tree in part (a) to reflect the op-tions now open with the market study. What should the medical professionals do now?

(d) What is the efficiency of the market study's information?

Reference no: EM132277043

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