The chair of the operations management department at Quality University wants to construct a control-chart for determining whether the four faculty teaching the basic OM course are in control with regard to the number of students who fail the course. Accordingly, he sampled 100 final grades from last year for each instructor, with the following results Instructor Number of Failures Prof. A 13 Prof. B 0 Prof. C 11 Prof. D 16 What are the 0.95 (5 percent risk of Type I error) upper and lower control limits for the control-chart? (Hint: First, select the best control chart type). 3. Weekly demand for a particular item averages 30 units, with a standard deviation of 4. This item is managed with a fixed-order-interval model. The order interval is three weeks, and this item has a certain lead time of one week. The desired service level is 97.5 percent. Assume that it is now time to place another order, and there are 43 units on hand. How many units should be ordered? 4. In the basic EOQ model, if annual demand doubles, what is the effect on the EOQ? Justify your answer. 5. Daily usage is exactly 60 gallons per day. Lead time is normally distributed with a mean of 10 days and a standard deviation of 2 days. What is the standard deviation of demand during lead time? 6. Lead time is exactly 20 days long. Daily demand is normally distributed with a mean of 10 gallons per day and a standard deviation of 2 gallons. What is the standard deviation of demand during lead time? 7. A manufacturer is contemplating a switch from buying to producing a certain item. Setup cost would be the same as ordering cost. The production rate would be about double the usage rate. Compared to the EOQ, what would be the economic production quantity? Explain why. 8. A manufacturer is contemplating a switch from buying to producing a certain item. Setup cost would be the same as ordering cost. The production rate would be about double the usage rate. Compared to the EOQ, what would be the maximum inventory? Explain why. 9. What are the basic steps in problem solving? Describe your recent achievement in which you have used these steps and solved a problem at your home or work. 10. Suppose you calculated the EOQ for Samsung phones to be 404 units. Assume that demand is normally distributed with average demand of 12 phones per day and a standard deviation of demand during lead time of 28 phones. If your phone supplier offers an average delivery lead time of 8 days and you want to maintain a Cycle Service Level of at least 95%, what is your reorder point?