V&A cafe started selling a popular drink that uses nonperishable coffee beans. The drink has a consistent flow of customers, but demand can fluctuate depending on the day. Customers are very loyal, and if V&A runs out, they are willing to wait until the next day i$.$e$.,$ their demands are backordered. Daily demand for the drink in terms of bags of coffee beans is distributed as N $(126\mathrm{.}5,16\mathrm{.}42).$ V&A orders the coffee beans from its supplier each morning. Unused beans held overnight incur a holding cost of $$0\mathrm{.}85$ per bag, and backorders incur a penalty of $$4\mathrm{.}25$ per bag. $($a$)$ Calculate the optimal base$-$stock level. $($b$)$ Assuming V&A cafe uses the base$-$stock level from part $($a$),$ calculate its type$-1$ service level. $($c$)$ Now assume that the that the supply lead time is $2$ days. Calculate the optimal base$-$stock level.