DigiSonic would also like to explore a more sophisticated forecasting method. They want you to consider exponential smoothing.

a$.$ Using simple exponential smoothing, compute three sets of forecasts for the sales of DigiSonic$$s

Blu$-$Ray discs, corresponding to $\backslash$alpha values of $0\mathrm{.}2,0\mathrm{.}5$ and $0\mathrm{.}8.$ Assume that the forecast for month

$1$ is $1376.(8$pt$)$

b$.$ To visually see the difference between forecasts and actual demand, plot the actual demand as

well as the three simple exponential smoothing forecasts computed in the same graph. Identify which value of $\backslash$alpha produces the most responsive forecast? What is the implication of this finding? $(4$pt$)$

c$.$ CalculatetheMAEandMeanAbsolutePercentageError$($MAPE$)$usingtheforecasterrorsfor each of these three sets of forecasts. Which $\backslash$alpha value seems to be most appropriate and explain why. $(3$pt$)$