The manager of a car wash received a revised price list from the vendor who su

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 four days but now the vendor promises a reduction of 25 percent in that time. Annual usage of soap is 4500 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 $30 and annual carrying cost is
$3 a gallon. The revised price list(cost per gallon) is shown in the following table:

Quantity unit price

1-399 $2

400-799 $1.70

800+ $1.62

a. What order quantity is optimal?