PROBLEM$-2.(60$ Pts$)$ WSX Automobile Spare Parts Store uses a $\backslash ((\backslash$mathrm$\{$Q$\},\backslash$mathrm$\{$R$\})\backslash )$ inventory system to control its stock levels. For a special "brake disc", historical data show that the distribution of monthly demand is approximately normal, with mean $14$ and standard deviation $4.$ Replenishment lead time for this paint is about $10$ weeks. Each can of paint costs the store TL$6.$ Although excess demands are back$-$ordered, the store owner estimates that unfilled demands cost about TL$10$ each in bookkeeping and loss$-$of$-$goodwill costs. Fixed costs of replenishment are TL$15$ 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? $(\backslash (\backslash$mathbf$\{35\}\backslash )$ Pts$)$

b$.$ What is the optimal safety stock for this paint? $(25$ Pts$)$