Daily demand for a certain product is normally distributed with a mean of 100 and a standard deviation of 50. The source of supply is reliable and maintains a constant lead time of 4 days. The cost of placing the order is $200, and the unit cost of the product is $40. The annual interest rate is 25% in this industry. Assume 360 days per year. a) Use the (s, S) policy, and find the order quantity and reorder point to satisfy a service level of 90%. What is the average inventory level? What is the annual cost? b) Suppose the manager wants to make it simple and sets the safety stock level equal to the average demand during the lead time. What is the annual total inventory-related cost? What is the coverage probability (service level)? How many times of stock-out do you expect per year? c) * Ignore the assumptions in (b). Recently, the retailer noticed the supplier became not so reliable. The lead time now is equally likely to be 2, 3, 4, 5, 6 days. Please find the order quantity and reorder point to satisfy a service level of 90%. What is the average inventory level? (You may first calculate the mean and standard deviation of the lead time.)