a) Plot the monthly sales data. b) Forecast January sales using each of the following: i) Naive method. ii) A 3-month moving average. iii) A 6-month weighted average using . 1,1.1,2,2, and : with the heaviest weights applied to the most recent month: iv) Exponential smoothing using an =.3 and a Septemic: forecast of 18 . v) A trend projection. c) With the data given, which method would allow you to formea: next March's sales? PXX -. D.9 Zimmerman's Bank is the only bank in the small town of St. Thomas. On a typical Friday, an average of 10 customers per hour arrive at the bank to transact business. There is one teller at the bank, and the average time required to transact business is 4 minutes. It is assumed that service times may be described by the exponential distribution. A single line would be used, and the customer at the front of the line would go to the first available bank teller. If a single teller is used, find: a) The average time in the line. b) The average number in the line. c) The average time in the system. d) The average number in the system. e) The probability that the bank is empty. A crew of mechanics at the Highway Department garage repair vehicles that break down at an average of 3 vehicles every 12 minutes (approximately Poisson in nature). The mechangic crew can service an average of 3 vehicles every 10 minutes with a repair time distribution that approximates an exponential distribution. The crew cost is approximately $100 per hour. The cost associated with lost productivity from the breakdown is estimated at $50 per hour. Which is cheaper, the existing system with one service crew or a revised system with two service crews? Note that the average waiting time for adding the second crew is 0.02