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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 4,500 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 $2.00

400−799 1.70

800 + 1.62

a. What order quantity is optimal?

b. What ROP is appropriate if the acceptable risk of a stockout is 1.5 percent?