$(20$ points$)$ A restaurant sells a snack food called Cheesy Blasters. Cheesy Blasters are essentially

nonperishable, and since they are a specialty item, customers who experience stockouts are willing

to wait until a future day, i$.$e$.,$ their demands are backordered. Daily demand for Cheesy Blasters

is distributed as $N(28\mathrm{.}3,{7\mathrm{.}1}^2).$ The restaurant orders the product from its supplier each morning.

Unsold Blasters held in inventory overnight incur a holding cost of $$0\mathrm{.}75$ per item, and backorders

incur a penalty of $$3\mathrm{.}50$ per item.

$($a$)$ Calculate the optimal base$-$stock level.

$($b$)$ Assuming the restaurant 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.