Problem $836207$:

Do not include anything other than numbers in your

responses. For example, do not include comma or dollar sign in your

numbers. As a rule of thumb, keep $2$ decimal places for larger

numbers and $3$ decimal places for smaller numbers less than

$1.$

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 $4$ days, but now the vendor

promises a reduction of $25$ percent in that time. Annual usage of

soap is $5990$ 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 $$35$ and annual carrying

cost is $$3$ a gallon. The revised price list $($cost per gallon$)$ is

shown in the following table:

$$

$$

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?$$