. (40 points) Suppose that you work as an engineer in the planning department of a company. You consider to forecast the demand for an item which exhibits a steady demand pattern. Based on your research, you find the following forecasting method: Weighted moving average (WMA) method is basically the same as simple moving averages, with one major exception. With weighted moving averages, the weight assigned to each past data point used in the calculation can vary. In this way, more influence can be given to some data points, typically the most recent demand point. The formulation is given below: ! = "!#" + $!#$ + + %!#% +& = 1 % &'" n is the number of periods being used. The demand pattern for that product for the past 10 months is given as D1, D2, D3, D4, D5, D6, D7, D8, D9 and D10, respectively. Suppose that the company had an initial forecast for month 1, say F1, before the beginning of month 1. Forecast the demand of period 11 using each of the following methods: a 3-month moving average; a 3- month weighted moving average using weights of w1, w2 and w3 (Make sure that the sum of three weights adds up to 1. Also make sure that more influence is given to more recent data, hence: w1>w2>w3); and exponential smoothing with a smoothing constant of a. Compute the MAD for each method and determine which method would be preferable under the circumstances. (Before solving the question, select an integer value from the given interval (except w1, w2, w3, a), fill in the following table and copy it into your answer sheet) Parameter Interval Selected value D1 [200; 300] D2 [200; 300] D3 [200; 300] D4 [200; 300] D5 [200; 300] D6 [200; 300] D7 [200; 300] D8 [200; 300] D9 [200; 300] D10 [200; 300] F1 [200; 300] w1 [0.1; 0.9] w2 [0.1; 0.9] w3 [0.1; 0.9] a [0.5; 0.9] Complete the suitable cells of the following table: Note: In your computations, do NOT round any numbers up or down. Please always use 2-digits for all non-integer values. (For instance: You can have a value such as 123.45 but not 123.4567) Period Actual demand Forecasts based on 3-month MA Forecasts based on 3-month WMA Forecasts based on exponential smoothing 1 2 3 4 5 6 7 8 9 10 11 N/A MAD