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# exam107 - ISyE 3232 Exam 1 Fall 2007 Name Please be neat...

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ISyE 3232 Exam # 1 Fall 2007 Name Please be neat and show all your work so that I can give you partial credit. GOOD LUCK. Question 1 Question 2 Question 3 Total 1

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(20) 1. Suppose that a bakery specializes in chocolate cakes. Assume the cakes retail at \$20 per cake, but it takes \$8 to prepare each cake. Cakes cannot be sold after one week, and they have a negligible salvage value. It is estimated that the weekly demand for cakes is: 15 cakes in 10% of the weeks, 16 cakes in 15% of the weeks, 17 cakes in 30% of the weeks, 18 cakes in 20% of the weeks, 19 cakes in 15% of the weeks, and 20 cakes in 10% of the weeks. (10) a. How many cakes should the bakery prepare each week to maximize its expected proﬁt? (20) b. What is the bakery’s expected optimal weekly proﬁt? 2
(30) 2. Suppose that jobs arrive at a machine at a rate 20/hour. Assume that the interarrival times are exponential (i.e. the probability density function f ( t ) = 20 e - 20 t ,t 0.) The service times have a mean of 2.5 minutes and a

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exam107 - ISyE 3232 Exam 1 Fall 2007 Name Please be neat...

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