Some negative absolute deviations looked weird. Please check all numbers. Thanks!

Problem 1 (Comparison of 4 Methods) (10 points) Your forecasting team is trying to determine what forecasting method to use for forecasting the future demand. The actual demand data for the past 12 weeks are recorded and provided in the following table. Please show your work to answer questions of a - f. WEEK ACTUAL DEMAND 1 72 2 75 3 77 4 78 5 81 6 83 7 86 8 88 9 88 10 90 11 94 12 95 a. Calculate the three-week simple moving average forecast for periods 4-12. (1 point) b. Calculate the three-week weighted moving average using weights of 0.5, 0.3, and 0.2 for periods 4-12. (2 points) c. Calculate the simple exponential smoothing forecast for periods 2-12 using an initial forecast (Fi) of 61 and an a of 0.30. (2 points) d. Calculate the exponential smoothing with trend forecast for periods 2-12 using an initial trend forecast (Ti) of 1.8, an initial exponential smoothing forecast (F1) of 60, an a of 0.30, and 8 of 0.30. (2 points) e. Calculate the mean absolute deviation (MAD) for the forecasts made by each method in periods 4-12. Which forecasting method do you recommend based on the MAD values? (2 points) f. Use the recommended forecasting method to predict the demand for next week, i.e., Week 13. (1 point) Exponential Smoothing Week (t) Actual Demand 3-week Simple Moving Average Absolute deviation 3-week Weighted Moving Average Absolute deviation Simple Exponential Smoothing, Ft Absolute deviation Ft Absolute deviation with Trend, FIT+ = Ft + Tt 60 NP 72 75 77 78 81 83 1.8 2.7 3.4 3.7 3.7 NM + Ooo 74.67 76.67 78.67 80.67 83.33 85.67 87.33 88.67 90.67 3.33 4.33 4.33 5.33 4.67 2.33 2.67 5.33 4.33 75.40 77.10 79.30 81.40 84.10 86.40 87.60 89.00 91.60 61.00 64.30 67.51 70.36 72.65 75.15 77.51 80.06 82.44 84.11 85.88 88.31 11.00 10.70 9.49 7.64 8.35 7.85 8.49 7.94 5.56 5.89 8.12 2.60 3.90 3.70 4.60 3.90 1.60 2.40 5.00 3.40 86 88 64.9 69.8 74.3 78.0 81.5 84.5 87.4 89.9 91.4 92.8 94.7 61.8 67.58 73.19 78.06 81.77 85.19 87.99 90.67 92.91 94.03 95.05 96.88 10.20 7.42 3.81 -0.06 -0.77 -2.19 -1.99 -2.67 -4.91 -4.03 -1.05 -1.88 3.7 3.5 3.3 3.0 2.6 2.2 2.1 88 90 94 95 10 11 12 6.69 MAD 4.07 3.46 7.39 -2.17