The owner of a small brewery in Milwaukee, WI$,$ is using Winters's method to forecast his quarterly beer sales. He has been using smoothing constants of $=0\mathrm{.}2,=0\mathrm{.}2,$ and $=0\mathrm{.}2.$ He has currently obtained the following values of the various slope, intercept, and seasonal factors: $,$ and $.$

a$)$ Determine the forecast for beer sales in quarter $11.$

b$)$ Suppose the actual sales turn out to be $128$ in quarter $11.$ Find and, and find the updated values of the seasonal factors. Also determine the forecast made at the end of quarter $11$ for quarter $13.$