A clothing company sells ski jackets every winter but must decide in the summer how many jackets to produce. Each jacket costs $65 to produce and ship and sells for $129 at retail stores. For the sake of simplicity, assume the jacket is sold in a single store. Customers who wish to buy this jacket but find it out of stock will buy a competitor's jacket; in addition to the lost revenue, the company also incurs a loss of goodwill cost of $15 for each lost sale. At the end of the winter, unsold jackets are sold to a discount clothing store for $22 each.

(a) First suppose that the demand for the ski jackets this winter will be distributed as a normal random variable with mean 900 and standard deviation 60. What is the optimal number of jackets to produce?

(b) Now suppose that the demand is distributed as a Poisson random variable with mean 900. What is the optimal number of jackets to produce?