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1. Betty Cooker runs a bakery in San Francisco that specializes in her famous Black Forest cakes. She estimates that the daily demand for this cake is normally distributed with a mean of 60 and a standard deviation of 20. Each customer wants to buy exactly one cake. Every day in the morning, Betty Cooker and her team of bakers prepare fresh batch of the cakes for sale that day. Her costs to bake and top each cake are $5. Each cake sells for $20. 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.
Suppose Betty wants to bake enough cakes so that she can be 99.0% sure that she can satisfy the demand of all of her customers. How many cakes should she prepare daily in the morning?
2. Betty Cooker runs a bakery in San Francisco that specializes in her famous Black Forest cakes. She estimates that the daily demand for this cake is normally distributed with a mean of 60 and a standard deviation of 20. Each customer wants to buy exactly one cake. Every day in the morning, Betty Cooker and her team of bakers prepare fresh batch of the cakes for sale that day. Her costs to bake and top each cake are $5. Each cake sells for $20. 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.
She hires a consultant, Max E. Mize, who advises her to, "Focus on maximizing your expected daily profits, and the customer demand will take care of itself." In order to maximize profits, how many cakes should Betty bake?
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