Question

PROBLEMS 1. A bookstore buys used textbooks and resells them. The demand for the books will be either 100, 150 or 200 copkes and the probabili ty of selling these nuabers. of books is 0.25. О.40 and 0.35 respectively. The book- store buys the used books for $8.00 and resells them for 10.50. (Assume the books will have no salvage value er this semester because a new edition will be ut.) Determine (a) The conditional payoffs and losses (b) The expected value for each alternative (c) How many books the bookstore should buy 2. Given the following decision tree, calculate the expected profit for ch of the three alternatives. Which alterna tive should be selected? -$15,000 +$8,500 $8,000 $10,000 Alternative 2 O.50) 0.20) $12,000 $17,000 $25,000 $16,000 (0.50) s12, ООО $35,000 (Probabilities) (Payoffs)

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Answer 1

Answer:

The demand for the books will be either 100, 150 or 200 books .

Therefore , the bookstore will definitely sell 100 books at least. It can sell more , but not exceeding 150 books.

Following table lists down probabilities of selling at least 100 or 150 or 200 books.:

Number of books	Probability that demand = X	Probability of selling the Xth unit
100	0.30	1
150	0.50	0.70
200	0.20	0.20
>150		0

In the given problem,

Cu = Cost of underaging per unit = Sale price/ unit – Purchase price / unit = $9 - $7.5 = $1.5

Co = Cost of overaging per unit = Purchase price / unit – Salvage price/unit = $7.5 – 0 = $7.5

Therefore , Critical ratio = Cu / ( Cu + Co) = 1.5 / ( 1.5 + 7.5) = 1.5/ 9 = 0.166

To maximize profit, one must by that quantity of X, so that :

P(X) = Critical Ratio ( or nearest to it in this case)

From the above table, it is evident that X = 150.

Therefore, to maximize profit one must by 150 books

THE BOOKSTORE MUST BUY 150 BOOKS TO MAXIMIZE PROFIT