Assignment 3 Production Planning and Inventory Control (10631431) Total marks: weight: 10 marks Due date: August 10h2020 at 12:00 pm to 1:00 pm Problem #1 (10 MARKS) 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. Formally the lead time was four days, but now the vendor promises a reduction of 50 percent in that time. Annual usage of soup is 5000 gallons. The car wash is open 300 days a year. Assume that daily usage is normal, and it has standard deviation of 4 gallons per day. The ordering cost is $40 and annual carrying cost is 25 percent of a unit price per gallon. The revised price list (cost per gallon) is shown in the table. Quantity Unit price 1-339 $10.00 400-799 $8.00 800 and more 56.00 a. What is the dollar value of the optimal order quantity? b. What ROP is appropriate if the acceptable risk of a stockout is 2.5 percent? c. How much safety stock should be held