Weis's paint store uses a $($Q$,$ R$)$ inventory system to control its stock levels. For a monthly demand is approximately normal, with mean $28$ and standard deviation $9$

Wrisculaty popular white latex po int$-$mai, with mean $28$ and standard deviation g

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?