Consider a retail store that uses the order$-$up$-$to model when ordering from its supplier. Orders are placed at the beginning of each week and received with a $4-$week lead time. Weekly demand follows a Poisson distribution with mean $0\mathrm{.}8.$

$[4$ points$]$ What is the average on$-$order inventory when the retail store uses an order$-$up$-$to level of S$=10?$

b$.[4$ points$]$ What is the average on$-$hand inventory when the retailer store uses an order$-$up$-$to level of S$=10?$

c$.$ what is the minimum order$-$up$-$to level required to achieve an in$-$stock probability of at least $99\mathrm{.}99\%?$

d$.[6$ points$]$ Suppose that parent company of this retail store has $16$ identical retail stores each facing the same demand as above and their inveinventorytory is pooled. So$,$ instead of each store ordering and holding its own inventory, inventory is shared from a common pool of inventory. What is the on$-$hand inventory to achieve an in$=$stock probability of at least $99\mathrm{.}99\%?$ Compare it to the toal on$-$hand inventory with $16$ stores but without pooling $($so$,16$ times the on$-$hand inventory corresponding to your answer in part c$)$ and explain the difference.