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 $56.$ 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?