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hmwk3 - ISyE 3232 H Ayhan J Dai Stochastic Manufacturing...

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ISyE 3232 Stochastic Manufacturing and Service Systems Spring 2011 H. Ayhan & J. Dai Homework 3 January 28, 2011 Due: at the start of class on Thursday, February 3 1. Suppose we are selling lemonade during a football game. The lemonade sells for $18 per gallon but only costs $3 per gallon to make. If we run out of lemonade during the game, it will be impossible to get more. On the other hand, leftover lemonade has a value of $1. Assume that we believe the fans would buy 10 gallons with probability 1/10, 11 gallons with probability 2/10, 12 gallons with probability 4/10, 13 gallons with probability 2/10, and 14 gallons with probability 1/10. (a) What is the mean demand? (b) If 11 gallons are prepared, what is the expected profit? (c) What is the best amount of lemonade to order before the game? (d) In what sense is that amount optimal? In other words, what was your objective function? (e) Instead, suppose that the demand was normally distributed with mean 1000 gallons and variance 200 gallons 2 . How much lemonade should be ordered?
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