The manager of a car wash received a revised price list from the vendor who supplies soap, and a promise of a shorter lead time for deliveries. Formerly the lead time was $2$ days, but now the vendor promises a reduction of $25$ percent in that time. Annual usage of soap is $6190$ gallons. The car wash is open $360$ days a year. Assume that daily usage is normal, and that it has a standard deviation of $4$ gallons per day. The ordering cost is $$45$ and annual carrying cost is $$3$ a gallon. The revised price list $($cost per gallon$)$ is shown in the following table:

Order Size Unit Price

$1--4492$

$450--7741\mathrm{.}7$

$775++1\mathrm{.}62$

The store manager is considering to provide a service level of $0\mathrm{.}6.$

How much is the Quantity from EOQ? $($Keep two decimal places$)$

How much is the total annual inventory related costs $($holding$,$ ordering, and purchase costs$),$ if the car wash order the quantity from EOQ model?

How much is the total annual inventory related costs $($holding$,$ ordering, and purchase costs$),$ if the bakery orders just enough to get the soap at the price of $$1\mathrm{.}7?$

How much is the total annual inventory related costs $($holding$,$ ordering, and purchase costs$),$ if the car wash orders just enough to get the soap at the price of $$1\mathrm{.}62?$

What is the car wash's optimal order quantity, given this quantity discount information?

How often $($in days$)$ should the car wash order?

How long $($in days$)$ is the lead time?

What is the Z value for the desired service level?

How much safety stock is needed to provide the desired service level?

What is the ROP for the desired service level?