ISyE 3232Stochastic Manufacturing and Service SystemsSpring 2011H. Ayhan & J. DaiHomework 3January 28, 2011Due: at the start of class on Thursday, February 31. Suppose we are selling lemonade during a football game. The lemonade sells for $18 per gallon butonly costs $3 per gallon to make. If we run out of lemonade during the game, it will be impossibleto get more.On the other hand, leftover lemonade has a value of $1.Assume that we believe thefans would buy 10 gallons with probability 1/10, 11 gallons with probability 2/10, 12 gallons withprobability 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 variance200 gallons2. How much lemonade should be ordered?
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