Demand for vanilla ice cream at a small lce cream shop can be approximated by a Normal distribution with a mean of $23$ Iitres per week and a standard devation of $4\mathrm{.}0$ 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 four days. The store is open seven days a week. Refer. z$-$values table.

$.$ If the EOQIROP model is used for ordering the Ice cream from the producer, what ROP would be consistent with the desired lead time service level? $($Round the thual answer to $2$ decimal pitacent$)$

ROP

litres

b$.$ If a fixed$-$interval model is used Instead, what order quantity should be used if the order interval is $9$ days and $11$ iltres are on hand and none are on order at the time of order? $($Do not round the internectlette cellculetions. Found the that enswer to the nearest Whole numberi

Quantity

litres

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 recelves a call from the producer saylng 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 $3$ 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 arrves? $($Round your Internedlate calculatlons to $2$ declmal places and the finel answer to $4$ clecimal placesis.$)$

Probabllity