The owner of a small brewery in Milwaukee, Wisconsin, is using Winters's method to forecast his quarterly beer sales. He has been using smoothing constants of $=\mathrm{.}2,=\mathrm{.}2,$ and $=\mathrm{.}2.$ He has currently obtained the following values of the various slope, intercept, and seasonal factors: $S_{10}=120,G_{10}=14,c_{10}=1\mathrm{.}2,c_9=1\mathrm{.}1,c_8=\mathrm{.}8,$ and $c_7=\mathrm{.}9.$

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

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