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 costs $26 a jar and requires a 3-month lead time for replenishment of stock. The replenishment time is constant. Harvey uses a 20% annual interest rate to compute holding costs. Bookkeeping expenses for placing an order amount to about $60. During the 3-month supply time, Harvey estimates that he sells an average of 150 jars but there is substantial variation. He estimates the standard deviation of demand for each 3-month period is 25. Assume that demand is described by a normal distribution.

a) What is the optimal order quantity?

b) How much safety stock should be maintained for 96% cycle service level?

c) What should be the reorder point for 96% fill rate?

d) Now suppose that the English company is ready to send the mustard by a faster ship, which will reduce the replenishment lead time to 1-month and the standard deviation of demand during that period to 14.4, but increase the cost to $32 per jar. What will be the new reorder point for 96% fill rate service level?

e) In order to achieve 96% fill rate service, what will be the optimal total inventory cost (Ordering + Holding + Purchase) before and after the decrease of lead time (and resultant price increase)? What managerial insights can you get from this?
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