1. Weekly demand for detergent at a Carrefour store is normally distributed, with a mean of 2,500 and a standard deviation of 1,000. The store manager continuously monitors detergent inventory and places a replenishment order of 9,000 units when there are 7,500 units in inventory. The supplier takes two and a half weeks to supply a Carrefour order. a) What CSL does the store achieve? State your answer with 3 decimal places. b) What fill rate does the store achieve? State your answer with 3 decimal places. c) What is the average flow time in weeks? State your answer with 1 decimal place. d) If the carrying cost of one unit in inventory for one year is $1.50, what is the annual carrying cost based on the above inventory policy?

2. Weekly demand for paper towels at a Target store is normally distributed, with a mean of 1,500 and a standard deviation 400. The supplier takes two weeks to supply a Target order, which is for a batch size of 9,000. Target is aiming for a fill rate of 98.5% and monitors its inventory continuously. a) How much safety inventory of paper towels should Target carry? Round your answer to the nearest integer. b) What should its ROP be?

3. Weekly demand for electric motors at a Japanese motor manufacturer is normally distributed, with a mean of 1,000 and a standard deviation of 1,000. Motors are currently assembled in China and delivered at a cost of 20,000 yen/motor. The supplier takes eight weeks to supply an order. A local Japanese manufacturer has offered to deliver motors with a lead time of one week at a cost of 20,400 yen per motor. The motor manufacturer is targeting a CSL of 98% and monitors its inventory continuously. The manufacturer incurs an annual holding cost of 30%. a) Should the manufacturer accept the local suppliers offer? b) Find the lead time of the Japanese manufacturer that would make both manufacturers equally attractive. State your answer with 2 decimal places.