A bakery prepares all its cakes between 4am and 6am so that they are fresh when customers arrive. The cost of baking a cake is $2 and selling price is $10. Demand for the day is estimated to be normally distributed with a mean of 20 and a standard deviation of 4.
a. If cakes are worthless if they are not sold on that day, what is the optimal number of cakes to bake?
b. If all day old cakes can be sold at a deeply discounted price of $1, how does that change the overage cost? What is the optimal number to bake?