Question 5: (30 points) The sound systems department of MediaMall is using a lot size-reorder point (Q, R) system to control the replenishment of a particular model of an iPod deck. The store sells an average of 100 decks each month. The monthly demand follows a normal distribution with a standard deviation of 10. The store pays $40 for each deck, which it sells for $80. The holding cost rate is 30 % per year. Fixed costs of replenishment amount to $98. If a customer demands the iPod deck when it is out of stock, the customer will generally go elsewhere. Replenishment lead time is two months. Currently, the store is using Q = 300 and R = 220. Compute: C. a. (5 points) the safety stock b. (5 points) the proportion of order cycles in which no stock out occurs (5 points) the proportion of demands that are not met d. (10 points) Determine the imputed shortage costs for (c) e. (5 points) what would be the optimal order quantity if there were no uncertainty in demand