IEOR150F10_hw04_sol

IEOR150F10_hw04_sol - IEOR 150, Fall 2010 Suggested...

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IEOR 150, Fall 2010 Suggested Solution to Homework 4 1. (a) The unit overage cost is c o = 0 . 08 - 0 . 03 = $0 . 05 and the unit underage cost is c u = 0 . 35 - 0 . 08 = $0 . 27. Therefore, the critical ratio is c u c o + c u = 0 . 84 , which is between 0 . 7 and 0 . 85, the cumulative probabilities of 20 and 25 bagels (c.f. Table 1). As we always do for discrete distributions, we round up to 25 bagels . This is the optimal baking quantity. Number of bagels Cumulative sold in one day Probability probability 0 0.05 0.05 5 0.10 0.15 10 0.10 0.25 15 0.20 0.45 20 0.25 0.7 25 0.15 0.85 30 0.10 0.95 35 0.05 1.00 a04 Table 1: Demand distribution for Problem 1 (b) Since 28 > 25, we should bake no additional bagel today. (c) Let x 1 = 0, x 2 = 5, . .., and x 8 = 35 be the possible realizations of the demand and p 1 = 0 . 05, p 2 = 0 . 1, . .., and p 8 = 0 . 05 be the corresponding probabilities. Then the mean is μ = 8 X i =1 p i x i = 18 bagels , and the standard deviation is σ = v u u t 8 X i =1 p i ( x i - μ ) 2 = 8 .
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IEOR150F10_hw04_sol - IEOR 150, Fall 2010 Suggested...

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