CQ EMBA Bagel and Coffee Shop

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The CQ EMBA Bagel and Coffee Shop is a small coffee shop with branches only in Ithaca and Kingston. They serve hungry CQ EMBA students as well as other townspeople who happen to drop in their stores. They have found the number of fresh raisin bagels demanded by their customers per day is uniform between 1 and 50 per day (i.e., they are equally likely to sell any number of bagels between 1 and 50). It costs Crazy, the owner of the coffee shop, 35 cents to make a raisin bagel and Crazy sells one for $1.00. Any bagels not sold the day they are made are discounted to 20 cents and sold as “day old” bagels. (Assume the demand for day-old bagels is separate from the demand for fresh bagels and that all day-old bagels are always sold).
a) How many raisin bagels should Crazy make each morning?
What is the probability that Crazy will have 2 or more unsold bagels leftover at the end of any given day if Crazy uses the optimal policy in Part a)?


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