Problem 2 (25 points total) A retail store wants to forecast their quarterly sales for sweaters in thousands of dollars for the first quarter of 2019. Two employees are debating about the best forecasting method to use. One employee believes that a four-period weighted moving average will work, but the second employee thinks that using seasonal relatives will yield a better forecast. In this problem, you will help the employees resolve their debate. Complete the following table with a four-period weighted moving average using weights of 0.7, 0.1, 0.1, and 0.1. The largest weight of 0.7 should be on the period farthest back in time and the remaining weights are for the periods closest in time to the quarter being forecast. For example, the forecast for Q1 2018 would place the weights 0.7, 0.1, 0.1, and 0.1 on the 2017 Quarters 1, 2, 3, and 4, respectively. Quarter Actual Sweater Sales (S) Forecast 4-period WMA Abs. Percent Error Q1 2017 20.0 Q2 2017 8.0 Q3 2017 2.0 Q4 2017 30.0 Q1 2018 17.0 18.0 5.9 Q2 2018 7.0 10.5 50.0 Q3 2018 1.0 6.8 580.0 Q4 2018 32.0 (a) (b) (a) (3 points): (b) (2 points) (c) (3 points) Using 4-period WMA method, what is the forecast for Q1 2019? (d) (2 points) What is the MAPE for this method? Complete the following table to setup the seasonal indices for this business. Quarter 2017 2018 Expected Sales Seasonal Index Average Quarterly Sales ($000) 18.5 Q1 20.0 17.0 14.6 1.26 Q2 8.0 7.0 7.5 14.6 0.51 Q3 2.0 1.0 1.5 14.6 0.10 Q4 30.0 32.0 (e) (f) (e) (2 points) (f) (1 points) (g) (2 points) (h) (5 points) Assume that using the seasonal method that we obtain forecasts of 18.0, 7.3, 1.5, and 30.2 for Quarters 1 through 4 of 2018, respectively. What would the MAPE be for this forecasting method? (1) (2 points) Assuming that a forecast of total sweater sales for 2019 has been made to be $58(000). What would the forecast for Q1 2019 be when using the seasonal index from above? 6) (3 points) Given the analysis for both the four-period weighted average and the seasonal indices, which forecasting method do you recommend? Why? List at least two reasons for the forecasting method that you choose