Harvey’s Specialty Shop is a popular spot that specializes in international gourmet foods. One of the items that Harvey sells is a popular mustard that he purchases from an English company. The mustard cost Harvey $10 a jar and requires a six-month lead time for replenishment of stock. Harvey uses a 20% annual interest rate to compute holding costs and estimates that if a customer requests the mustard when he is out of stock, the loss-of-goodwill cost is $25 a jar.

Bookkeeping expenses for placing an order amount to about $50. During the six-month replenishment lead time, Harvey estimates that he sells an average of 100 jars (λτ=100), but there is substantial variation from one six-month period to the next. He estimates that the standard deviation of λ during each six-month period is 20.

Assume that demand is described by a normal distribution. Harvey would like to find the optimal replenishment size to restock mustard jars. He starts with an order size equal to EOQ, and find a reorder point R and the expected number of shortages n(R) associated with R.

(a) What is the value of R? Show all steps and calculations.

(b) What is the value of n(R)? Show all steps and calculations.

(c) Using the answers obtained in (a) and (b), find the new order size. Show all steps and calculations.