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# hmwk2 - them at 40 cents per pound during the week Bananas...

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ISyE 3232 Stochastic Manufacturing and Service Systems Fall 2011 H. Ayhan Homework 2 August 30, 2011 Due: at the start of class on Wednesday, September 7 1. Let D be a discrete random variable with the following pmf. P ( D = k ) = 1 / 10 if k = 5 2 / 10 if k = 6 2 / 5 if k = 7 2 / 10 if k = 8 1 / 10 if k = 9 0 otherwise . Find a) E [min( D, 7)] . a) E [(7 D ) + ] . (Recall that (7 D ) + = max { 7 D, 0 } ). 2. Now assume that D is a continuous random variable and uniformly distributed between 5 and 10. Find a) E [max( D, 8)] . a) E [( D 8) ] . 3. David buys fruits and vegetables wholesale and retails them at Davids Produce on La Vista Road. One of the more di cult decisions is the amount of bananas to buy. Let us make some simplifying assumptions, and assume that David purchases bananas once a week at 10 cents per pound and retails
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Unformatted text preview: them at 40 cents per pound during the week. Bananas that are more than a week old are too ripe and are sold for 5 cents per pound. Suppose the demand for the good bananas follows the same distribution as D given in the ±rst question. What is the expected pro±t of David in a week if he buys 7 pounds of banana? 4. Now assume that the demand for the good bananas is uniformly distributed between 5 and 15. What is the expected pro±t of David in a week if he buys 7 pounds of banana? 5. Find the expected pro±t if David’s demand for the good bananas follows an exponential distribution with mean 7 and if he buys 7 pounds of banana....
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