The GPI bookstore orders sweaters with the GPI logo on them, and sells them for $40 a piece. During a typical month, 80 sweatshirts are sold (this includes all sizes and styles ordered from a particular supplier). It costs $25 to place an order, and 20 percent to carry sweatshirts in inventory for a year.

a. How many sweatshirts should the bookstore order at a time?

b. Because of variations in demand, the GPI bookstore has discovered that it should establish a safety stock for its sweatshirts. It wants to use a reorder point system with two-week lead time. The weekly demand is 20 units on average with a standard deviation of 5 units.What reorder point should the bookstore establish to ensure a 95% service level?(hint: the lead time is constant, but the demand is stochastic).

c. How much inventory will the bookstore carry on average? (hint: add the safety stock to the average cycle inventory calculated from the EOQ)

d. What would be the reorder point if the service level is increased to 99%?

e. What would be the reorder point is the lead time is reduced to one week?