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.
Aswer the following questions. Show your work to receive full credits.
1.(3 points) How many cakes should Betty prepare daily in the morning if she wantsto achieve a service level of 0.9?
2.(5 points) Based on what you’ve learned in OPRE 301, how many cakes shouldBetty bake to maximize her expected profit?
3.(7 points) Betty lately learnt that she could sell the leftover cakes to a nearby clubat a price of $6 with probability 0.8. The remaining cakes will then be given awayto the kitchen. With this reselling opportunity, how many cakes should Bettyprepare daily to maximize the expected profit?
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