The manager of car wash received revised price list from the vendor who supplies soap, and promise of shorter lead time for deliveries. Formerly the lead time was 4 days, but now the vendor promises the reduction of 25 percent in that time. Annual usage of the soap is 4500 gallons. The car wash is open 360 days a year. Suppose that daily usage is normal, and that it has the standard deviation of 2 gallons for each day. The ordering cost is $30 and annual carrying cost is $3 a gallon. The revised price list (cost per gallon) is given in the following table:
Quantity

unit price

1399

$2

400799

$1.70

800+

$1.62

a. What order quantity is optimal?