Sheri is a car distributor in a rural area. She has customers that own relatively old cars. To main- tain good customer service, Sheri keeps a small inventory of spare parts for old-model cars. One item is brake boosters. It is a slow-moving item, and therefore she uses the periodic review policy with a review period of two months. The annual demand for booster sets has a normal distribution with mean of 15 and standard deviation of 5. Because this item is out of production, delivery lead time is five months. The cost of a set of boosters is $500. Sheri places high value on maintaining customer satisfaction. Therefore, she considers goodwill to be crucial, and estimates the shortage cost to be $5000. Shortages are backlogged, and annual inventory holding cost is 20 percent. (a) Find the optimal target inventory. (b) Find the implied service level for policy I and policy 2. Discuss. (c) Find the safety stock for a set of brake boosters. (d) Find the expected annual cost of the periodic review policy. (e) Suppose a continuous review policy is used. Find the safety stock.