Weiss’s paint store uses a (Q, R) inventory control system to control its stock level. For a particular popular white latex paint, historical data show that the distribution of monthly demand is approximately normal, with mean 28 and standard deviation 8. Replenishment lead time for this paint is about 14 weeks. Each can of paint costs the store $6. Although excess demands are backordered, the store owner estimates that unfilled demands cost about $10 each in bookkeeping and loss of goodwill costs. Fixed costs of replenishment are $15 per order, and holding costs are based on a 30% annual rate of interest. 1. What are the optimal lot size and reorder point for this brand of paintso that the expected total cost per unit time can be minimized?
2. What is the optimal safety stock for this paint?(Assume one month has four weeks)