For the I-75 Discount Carpet Store, suppose that monthly demand for Super Shag carpet stocked by the store is normally distributed with an average monthly demand of 28 yards and a standard deviation of 2 yards of carpet per month. The lead time for receiving a new order of carpet is 14 weeks. Each yard of carpet costs the store $6. Although excess demands are backordered, each unit of stock-out costs about $10 due to bookkeeping and loss-of-goodwill. Fixed cost of replenishment is $15 per order and holding costs are based on a 30% annual interest rate. a) Use a (Q, R) inventory system to determine the optimal lot size (order quantity), reorder level and the expected inventory level (safety stock) just before an order arrives. [Hint: R = oz +u] (10 marks) b) If the store wants a service level of 95 percent with the probability of a stockout equal to 5 percent, determine the reorder point and safety stock. [Hint: R = (5 marks) dL+ zoa VL]