QWell, located in Guelph, is a large online retailer of refillable water bottles. QWell operates 300 days a year and sells an average of 280 one litre water bottles a day. They order bottles from a manufacturer in China. After ordering, bottles are always shipped within exactly 18 days. Annual holding costs per bottle are estimated to be 15% of the cost of bottles. The ordering cost is $100 per order. The cost of a one litre bottle is $4.

a. What is the economic order quantity (EOQ) for QWell? What is the average inventory? What is the expected total number of orders per year?

b. What are the total annual holding costs of the stock for QWell? What are the total annual ordering costs? Using an appropriately labelled diagram, graph setup cost, holding cost, and total inventory cost, and show the optimal economic order quantity (EOQ) and the minimum total inventory cost.

c. If QWell orders in quantities of 6,000 or more, it can get a $0.20 discount per bottle. Should QWell take the quantity discount? How much should QWell order?

d. Now assume that the demand for the water bottles is normally distributed with a variance of 25 bottles per day, and lead time is assumed to be normally distributed with a variance of 4 days (instead of the fixed numbers given above). Assume that management has specified that no more than a 5% risk of a stockout is acceptable. What is the standard deviation of demand during lead time? What is the safety stock needed to attain a 5% risk of stockout during lead time? What is the demand during lead time? What should be the reorder point? What is the annual holding cost of maintaining the level of safety stock needed to support a 5% risk of a stockout?