Demand for vanilla ice cream at a small ice cream shop can be

approximated by a Normal distribution with a mean of $21$ litres per week

and a standard deviation of $3\mathrm{.}5$ litres per week. The ice cream is

purchased from an ice cream producer. The store manager desires a lead

time service level of $90$ percent. Lead time from the producer is two days.

The store is open seven days a week. LO$4$ & LO$5$

a$.$ If the EOQ$/$ROP model is used for ordering the ice cream from the

producer, what ROP would be consistent with the desired lead time

service level?

b$.$ If a fixed$-$interval model is used instead, what order quantity should be

used if the order interval is seven days and $8$ litres are on hand andPage $441$

none are on order at the time of order?

c$.$ Suppose that the manager is using the EOQ$/$ROP model described in$$part a$.$ One day after placing an order with the producer, the manager$$receives a call from the producer saying that the order will be delayed$$because of problems at the producer$$s plant. The producer promises to$$have the order there in two days. After hanging up$,$ the manager$$checks the inventory of vanilla ice cream and finds that $2$ litres have$$been sold since the order was placed. Assuming that the producer$$s$$promise is valid, what is the probability that the store will run out of$$vanilla ice cream before the shipment arrives?