$2.\backslash (\backslash$mathbf$\{(15+15)\}\backslash )$ Spools'R'Us Manufacturing company produces different types of spools. Demands for bob spools $($in $\backslash (10^\{3\}\backslash )$ units$)$ over the last $6$ months $(2024)$ are as follows:

a$)$ Qualified for short time forecasting period, the industrial engineer of Spools'R'Us decided to use simple exponential smoothing methods for forecasting. For this data set, determine the optimal $\backslash (\backslash$alpha $\backslash )$ value with two decimal place variations ONLY.

b$)$ With the optimal $\backslash (\backslash$alpha $\backslash )$ value you determined in part a$,$ if adjusted exponential smoothing method is preferred, for this data set, determine the optimal $\backslash (\backslash$beta $\backslash )$ value with two decimal place variations ONLY.

Note: This manufacturing company uses percentage deviation $($MAPD$)$ as a tool for justifying and utilizing a specific technique and$/$or a set of parameters.