### The manager of a car wash received a revised price list

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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 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 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?

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