PROBLEM # 4 (25 points) Nittany Colors paint store is a famous paint shop in State College, Pennsylvania. One of the most popular paints at this paint store is a blue eggshell latex paint. Historical data show that the distribution of annual demand for this paint is approximately normal, with mean of 3,600 cans and variance of 384 cans. Replenishment lead time for this paint from a wholesaler is about two months. The administrative cost of placing an order is $1,000. For each can of this paint, the holding cost is $5 per month and the shortage cost is estimated to be $15 per month. The store's inventory manager is interested in using the stochastic continuous-review (R, Q) inventory policy with a service level corresponding to a probability of 0.8997 that stockout will not occur between the time an order is placed and the time the order is received. (a) (12 points) Determine the optimal values of the reorder point (R) and optimal order quantity (Q) that minimize the expected inventory cost per time unit. (Note: Please, refer to the standard normal table at the last page.) (b) (5 points) What will be the desirable safety stock (SS)? (c) (8 points) What will be the average number of stockouts per year with this inventory policy