Dan McClure owns a thriving independent bookstore in artsy New Hope, Pennsylvani

Question

Dan McClure owns a thriving independent bookstore in artsy New Hope, Pennsylvania. He must decide how many copies to order of a new book, Power and Self Destruction, an exposé on a famous politician's lurid affairs. Interest in the book will be intense at first and then fizzle quickly as attention turns to other celebrities. The book's retail price is $21, and the wholesale price is $11. The publisher will buy-back the retailer's leftover copies at a full refund, but McClure Books incurs $3 in shipping and handling costs for each book returned to the publisher. Dan believes his demand forecast can be represented by a Normal distribution with mean 200 and standard deviation 60

Explanation / Answer

Purchase price of the book by the retailer = C = $11

Sales price of the book by the Retailer = S = $21

Sala price of the book = $ 11 ( full refund ) - $ 3 ( shipping and handling cost) = $ 8

Thus,

Underage cost = Cu = S – P = 21 – 11 = 10

Overage cost = Co = 11 – 8 = 3

Hence,

Critical ratio = Cu / Cu + Co = 10 / ( 10 + 3 ) = 10/13 = 0.7692

Critical ratio is equal to the probability of the optimum quantity to be ordered .

Thus corresponding Z value for the probability 0.7692 = NORMSINV ( 0.7692 ) = 0.736

Thus ,

Optimum quantity to be ordered

= Mean demand + z value x Standard deviation of demand

= 200 + 0.736 x 60

= 200 + 44.16

= 244.16 ( 244 rounded to nearest whole number )

244 COPIES ARE TO BE ORDERED FOR THE NEW BOOK

244 COPIES ARE TO BE ORDERED FOR THE NEW BOOK

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