An automotive warehouse stocks a variety of parts that are sold at neighborhood stores. One particular part, a popular brand of oil filter, is purchased by the warehouse for $1.50 each. It is estimated that the cost of order processing and receipt is $100 per order. The company uses an inventory carrying charge based on a 28 percent annual interest rate. The monthly demand for the filter follows a normal distribution with mean 320 and standard deviation 81. Order lead time is assumed to be five months. Assume that if a filter is demanded when the warehouse is out of stock, then the demand is back-ordered, and the cost assessed for each back-ordered demand is $12.80. Determine the following quantities: a. The optimal values of the order quantity and the reorder level. b. The average annual cost of holding, setup, and stock-out associated with this item assuming that an optimal policy is used. c. Evaluate the cost of uncertainty for this process. That is, compare the average annual cost you obtained in part (b) with the average annual cost that would be incurred if the lead time demand had zero variance. d. Suppose that the stock-out cost is replaced with a Type 1 service objective of 95 percent. Find the optimal values of (Q, R) in this case. e. Suppose that a Type 2 service objective of 95 percent is substituted for the stock- out cost of $12.80. Find the resulting values of Q and R. Also, what is the imputed cost of shortage for this case