The manager of a car wash received a revised price list from the vendor who supplies soap, anda promise of a shorter lead time for deliveries. Formerly the lead time was four days, but now thevendor promises a reduction of 25 percent in that time. Annual usage of soap is 4,500 gallons. Thecar wash is open 360 days a year. Assume that daily usage is normal, and that it has a standarddeviation 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 Price1−399 $2.00400−799 1.70800 + 1.62a. What order quantity is optimal?b. What ROP is appropriate if the acceptable risk of a stockout is 1.5 percent?

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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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?

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