Suppose you operate a store. The weekly average demand for an item sold in your store is 20 units. Your upstream supplier charges $100 for each item sold to you. The annual holding cost is 20% of the item cost. It costs $160 to place an order. The lead time is 1 week and your store operates 50 weeks per year. For all the answers, round UP to integers. (a) What is the optimal order quantity? (5 points) (b) Suppose you want to achieve a 95% service level during the lead time, and the weekly demand is normally distributed with a mean of 20 units and standard deviation of 10 units. What will be your reorder point? What will be the safety stock level? What is your average inventory? Note: default case does not include pipeline inventory. (5 points) (c) Suppose you want to achieve a 95% service level during the lead time, and the distribution of weekly demand is listed in the following table. What will be your reorder point? What will be the safety stock level? (5 points) Number of units 15 16 17 18 19 20 21 22 23 24 25 Probability 0.01 0.03 0.08 0.1 0.18 0.26 0.14 0.07 0.05 0.04 0.04