$3.$ Weiss 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 $$6.$ Although excess demands are back ordered, the store owner estimates that unfilleddemands cost about $$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 brand of paint?