Weiss Paint store uses a (Q,r) inventory system to control its stock levels. For a particular popular white latex paint, historical data shows that the monthly demand is approximately normal with mean 28 and standard deviation of 8. Replenishment lead time for this paint is about 14 weeks. Each can of paint costs the store owner $6. Although excess demands are back ordered, store owner estimates that unfilled demands cost about $10 in bookkeeping and lost good will. Fixed costs of replenishment are $15 per order and holding costs are based on a 30% annual rate of interest. a) What is the optimal lot sizes and reorder point for this brand of paint. ? b) What is the optimal safety stock for this paint? c) The owner decides that his stockout cost of $10 may not be accurate and decides to switch to a service level model, and decides to set his order quantity using the EOQ model, and determine the reorder point so that there is stock out in 90% of the order cycles. What is the resulting (Q,r) values. ? What is the fill rate that he would achieve using this policy. d) Suppose he desires a fill rate of 95% what is the optimum (Q,r).