Demand for vanilla ice cream at a small ice cream shop can be approximated by a Normal distribution with a mean of $25$ litres per

week and a standard deviation 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 two days. The store is open seven days a week. Refer:

$z-value{s}_{?}$ table.

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? $($Round the final answer to $2$ decimal places.$)$

ROP

litres

b$.$ If a fixed$-$interval model is used instead, what order quantity should be used if the order interval is $7$ days and $7$ litres are on hand

and none are on order at the time of order? $($Do not round the intermediate calculations. Round the final answer to the nearest

whole number.$)$

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 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 $1$ 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? $($Round your intermediate calculations to $2$ decimal places and

the final answer to $4$ decimal places.$)$

Probability