Problem 836202: Do not include anything other than numbers in your responses. For example, do not include comma or dollar sign in your numbers. As a rule of thumb, keep 2 decimal places for larger numbers and 3 decimal places for smaller numbers less than 1. 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 2 days, but now the vendor promises a reduction of 25 percent in that time. Annual usage of soap is 5460 gallons. The car wash is open 360 days a year. Assume that daily usage is normal, and that it has a standard deviation of 3 gallons per day. The ordering cost is $50 and annual carrying cost is $4 a gallon. The revised price list (cost per gallon) is shown in the following table:

Order Size	Unit Price
1--449	2
450--724	1.7
725++	1.62

1. What is the car wash's optimal order quantity, given this quantity discount information? 2. How often (in days) should the car wash order? 3. How long (in days) is the lead time? What is the ROP for the desired service level? 4. What is the Z value for the desired service level? How much safety stock is needed to provide the desired service level?