Harry\'s Comic Book store is trying to decide on how many copies of a book to pu

Question

Harry's Comic Book store is trying to decide on how many copies of a book to purchase at the startof the upcoming selling season. The book retails at $30.00. The publisher sells the comic book to Harry at $22.00. Harry will dispose of all of the unsold copies of the book at 50% off the retail Price, at the end of the season. harry estimate3s that demand for this book during the season is Normal with a mean of 1200 and a standard deviation of 450. The publisher is thinking of offering the following scheme to Harry. At the end of the season, they will buy back unsold copiess at a Pre-determined price of $18.00. However, Harry would have to bear the costs of shipping unsold copies back to the publisher at $1.50 Per copy. What is the quantity that Harry should Order, to maximize his expected Profits?

Explanation / Answer

The cost of underestimating the demand is Cu and cost of overestimating demand is Co Cu = $30 - $22 = $8 Co = $22 - $18 + $1.50 = $5.50 Service Level = Cu / (Cu + Co) = 8 / (8 + 5.50) = 8 / 13.50 = 0.5926 Z Value at above service level = 0.2342 Optimal Order quantity = Mean + Z Value * Std Deviation = 1200 + 450 * 0.2342 = 1200 + 105.39 = 1305.40

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