The [manager of a car wash has received a revised price list from the vendor of the liquid 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 (i.e., new lead time is 3 day's).
Annual usage of soap is 4,500 litres. The carwash is open 360 days a year. Assume that daily usage of soap is Normal, and that it has a standard deviation of two litres per day. The ordering cost is $10 per order and annual holding cost rate is 40 percent of unit cost. The revised price list (cost per litre) is shown below.

a. What order quantity is optimal?
b. What ROP is appropriate if the acceptable risk of a stock-out is 1.5 percent?

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Quantity itres Unit Price per litre 1-399 400-799 800+ $2.00 1.80 1.60