8) You run an auto shop where you replace old hybrid batteries with new ones purchased from manufacturers located overseas. You are going to shut shop for the winter in two weeks, and therefore, must place your last order of hybrid batteries for the year (orders take a week to reach you). The manufacturer charges you $1200 for each battery, and you charge your customers $1400 for each battery exclusive of labor. However, these batteries will be replaced by a new model next year, and therefore, any batteries left over from your current purchase will only be worth $900 when you reopen your shop next year. Weekly demand is 100 units with probability 0.25, 200 units with probability 0.6, and 300 units with probability 0.15.

a) If you want to offer a service level of 80% in your last week of operation, how many batteries should you order? (5 points)

b) What is the optimal service level, and optimal number of batteries to order?

(10 points)