Betty Cooker runs a bakery in San Francisco that specializes in Black Forest cakes. She estimates that the daily demand for cakes is Normally distributed with mean 50 and standard deviation 20.Every morning, Betty Cooker and her team of bakers prepare a fresh batch of cakes for sale that day.Her cost to bake each cake is $5.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 (i.e., the salvage cost of unsold cakes is zero).

How many cakes should Betty manufacture daily in the morning to maximize expected profits? Choose thenumericallyclosest answer.

Suppose Betty incurs a cost of $1 per cake in terms of handling and transporting the unsold cakes to the soup kitchen. Then, the optimal number of cakes she now prepares daily in the morning to maximize expected profits will be...