FINAL EXAM Quantitative Methods and Research Spring 2017 1. Demand for a popular athletic shoe is nearly constant at 800 pairs per week for a regional division of a national retailer. The cost per pair is $54. It costs $72 to place an order, and annual holding costs are charged at 22% of the cost per unit. The lead time is two weeks. For 4 points each, answer the following questions: a. b. c. d. 2. What is the EOQ? What is the reorder point? What is the cycle time? What is the total annual inventory cost? The Tiernan Gallery and Art Museum distributes to its visitors a printed guide to its collections. There are about 18000 visitors per year. Holding costs for the brochures are 20% and it costs $30 to place an order with the printer. The printer has offered the following discount schedule: Category 1 2 3 Order Size 0 - 1499 1500 - 2999 3000 and over Unit Cost $2.50 $2.20 $1.80 For 11 points, how many brochures should be printed at a time? 3. A weekly sports magazine publishes a special edition for the World Series. The sales forecast is for the number of copies to be normally distributed with mean 800,000 copies and standard deviation 60,000 copies. It costs $.35 to print a copy, and the newsstand price is $1.95. Unsold copies will be scrapped. For 11 points, how many copies should be printed? 4. Bank Y has a single-channel waiting line, assume the mean arrival rate of 6 customers per hour and the mean service rate for a bank worker is 8 customers per hour. For 3 points each, answer the following questions: A. B. C. D. E. F. What is the probability that the bank worker will be idle? What is the average number of customers in the system? What is the average time a customer spends in the systems? What is the average number of customers in the queue? What is the time a customer spends in the queue waiting for service? What is the probability an arriving customer will have to wait? 5. From the schedule of activities listed below, for 11 points draw the PERT/CPM network. Activity A B C D E F G 6. Immediate Predecessor --A B B A C, D E, F Given the following network with activities and times estimated in days, D A Start E B F C G H I J K Finish Activity A B C D E F G H I J K Optimistic 2 1 6 5 3 8 4 3 5 12 1 Most Probable 5 3 7 12 4 9 6 6 7 13 3 Pessimistic 6 7 10 14 5 12 8 8 12 14 4 For 6 points each, answer the following questions: a. b. c. 7. What are the critical path activities? What is the expected time to complete the project? What is the probability the project will take more than 28 days to complete? The number of rolls of film processed each quarter by a one-hour photo finishing shop has been recorded for the last four years. Quarter 1 2 3 4 Year 1 942 853 896 915 Year 2 1006 893 947 981 Year 3 1109 946 962 1051 Year 4 1243 1067 1102 1177 For 5 points each, answer the following questions: a. b. c. Graph the time series. Does a linear trend appear? Develop the equation for the linear trend component for the time series (Trend Projection only, calculating seasonal components are not required). Use the linear trend developed in part (b) to prepare a forecast for sales in year 5