Question $1$

Problem $836206$:

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 $8$ days, but now the vendor

promises a reduction of $25$ percent in that time. Annual usage of soap is $4620$ gallons. The car wash is

open $360$ days a year. Assume that daily usage is normal, and that it has a standard deviation of $2$

gallons per day. The ordering cost is $$35$ and annual carrying cost is $$4$ 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 $0\mathrm{.}55.$

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?