John manages a convenience store in which he sells phone cards to consumers. He purchases the phone cards from a distributor at $2 each, and pays a fixed $37.50 shipping and handling charge per order. The lead time from his distributor is 2 weeks. Assume an annual rate of 25% for inventory carrying charges and 50 weeks per year. Weekly demand is normally distributed with a mean and standard deviation of 300 and 14 phone cards respectively. Assume full backorders.
(a) What is the optimal order quantity?
(b) Suppose that Justin wants to provide a 90% service level. What is the optimal reorder point?