Problem # $1-$ Jackson Manufacturing Corporation $(30$ points$)$ Management of the Jackson Manufacturing Corporation wishes to choose a forecasting method for forecasting total sales for the corporation. Total sales $($in million of dollars$)$ for each month of the last year are shown below. Forecast sales using the na$$ve method and four$-$month simple moving average. Compare MAD and MSE values and provide your recommendation. Using initial estimates of $120($i$.$e$.$ F$1=120),$ apply exponential smoothing with a smoothing constant alpha equal to $0\mathrm{.}1,0\mathrm{.}3$ and $0\mathrm{.}5$ to forecast sales. Compare both MAD and MSE for these three values of the smoothing constant alpha and provide your recommendation. Using initial estimates of $120$ for the average value and $10$ for the trend $($i$.$e$.$ F$1=120,$ T$1=10),$ apply exponential smoothing with trend adjustment $($i$.$e$.$ double exponential smoothing$)$ to forecast sales. Use combination of the smoothing constant alpha equal to $0\mathrm{.}3$ or $0\mathrm{.}5$ and betta equal to $0\mathrm{.}3$ or $0\mathrm{.}5.$ Compare MAD and MSE for these four combinations and provide recommendation. Which one of the above forecasting methods would you recommend that management use? Using this method, what is the forecast of total sales for January of the new year? The shift in total sales from month to month is due to the release of new products on top of a stable product base. Given this fact, how might the quantitative approach to forecasting total sales be improved? Describe the role of managerial judgment in applying the quantitative approach developed$/$suggested in part $.$ Be specific in your response. Month anuary February March April May June Sales $126137142150153154$ Month July August September October November December Sales $148145147151159166$