Problem $836210$:

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: