Freeport Corporation finds that demand for surfboards has average demand of 13 units per day, with a standard deviation of 4 units. Lead time from the supplier averages 12 days, with a standard deviation of 3 days. The item costs $53 and the inventory carrying cost is 30 percent. Use Table 7-2.
a. Suppose management decides to offer a 97.5 percent service level; that is, it is willing to experience a stockout probability of 2.5 percent during the order cycle. How much safety stock should be carried? (Do not round intermediate calculations. Round up your answer to the next whole number.)
b. How much is the annual inventory carrying cost of the safety stock because of this decision? (Round your answer to the nearest dollar amount.)
c. You decide that you want this company to give better service to its customers. You decide that a 97.72 percent service level is appropriate. How much safety stock must be carried to offer this service level? (Do not round intermediate calculations. Round up your answer to the next whole number.)
d. What is the additional inventory carrying cost that will be incurred on this item because of your decision to increase the service level? (Round your answer to 2 decimal places.)
e. What will the reorder point be for the company if your decision is implemented? (Round your answer to the nearest whole number.)