Problem 4. (15 points) Betty Cooker runs a bakery in Cleveland that specializes in her famous Black Forest cakes. A popular type of frosting is Devilicious. Every day in the morning, Betty and her team of bakers prepare a fresh batch of the cakes for sale that day. Her total cost to bake and top each cake is $8. Each cake sells for $15. Betty’s Bakery prides itself on its fresh assortment, so cakes not sold by the end of that day are given away to a soup kitchen for the homeless.
Based on historical data, Betty estimates that the daily demand for Devilicious has the following distribution:
1. (3 points) How many cakes should Betty prepare daily in the morning if she wants to achieve a service level of 0.9?
2. (5 points) Based on what you’ve learned in OPRE 301, how many cakes should Betty bake to maximize her expected profit?
3. (7 points) Betty lately learnt that she could sell the leftover cakes to a nearby club at a price of $6 with probability 0.8. The remaining cakes will then be given away to the kitchen. With this reselling opportunity, how many cakes should Betty prepare daily to maximize the expected profit?
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