Weiss’s paint store uses a (q, r) inventory system to control its stock levels. for a particularly 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 back-ordered, 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 percent annual rate of interest.
a. what are the optimal lot sizes and reorder points for this brand of paint?
b. what is the optimal safety stock for this paint?