r Part C: Quantitative/Chart/Graph Questions [90 points]. Answer all questions in this part in the paper provided. Show all work for full credit. Question 1 (Statistical Process Control) [15points]: The table below shows data for a process where fifteen samples were taken with four units per sample. Using these data construct X and R charts assuming three-sigma control limits for the charts indicating all UCL and LCL levels on the charts. Does the process appear to be in control and stable? If yes why, ifno why not? - - Sample Each Unit in Sample 1 10.11 10.16 9.93 9.87 2 10.07 9.98 9.99 10.03 3 10.00 10.08 10.02 4 10.06 9.99 0.10 5 10.02 10.09 10.10 10.00 10.06 10.05 6 9.91 9.99 10.00 9.97 7 9.98 10.05 10.05 9.92 8 10.01 10.06 10.05 10.08 9 10.00 9.91 10.01 9.98 10 10.01 10.08 10.08 9.91 11 10.00 10.04 9.98 10.06 12 10.04 9.91 9.95 9.92 13 10.00 10.05 9.99 10.08 14 9.80 10.00 9.96 9.89 15 9.97 10.09 9.91 10.08 Question 2 (Inventory Control) [15 points]: A manager at a widget company oversees a warehouse serving multiple retail stores. She has the following data with which to determine the optimum order amount for the warehouse using a fixed-order quantity model. Demand is 292,000 widgets per year, ordering cost is $20.00 per order, inventory holding cost is $.80 per widget per year, lead time is 14 days, and cost per widget is $8.00. With this information answer the following questions: A. What is the optimal order size Qopt ? B. What is the reorder point? C. What is the annual ordering cost? D. What is the average holding cost per order? E. What is the total cost? Widgets are wildly popular. If the company's retail stores ever ran out it would result in extremely bad publicity. Consequently, the manager's boss wants the manager to establish a safety stock level at the warehouse. It is known that average inventory follows a normal distribution and that the daily standard deviation of usage during lead time (ad) is 40. The manager wants the probability of not stocking out during lead time to be approximately 98%. F) Given these data, what is the safety stock level? G) What is the new reorder point