Problem $1.$ Remember the forecasting problem faced by The Coffee Shop around the Corner $($CS$)$ that you worked on in the last homework: Hank, the owner of CS$,$ would like to forecast the demand for muffins, which shows a significantly seasonal pattern in the course of a day. Suppose you decided to use Winter's method to forecast the demand during Day $4.$ Assume $\backslash (\backslash$alpha$=0\mathrm{.}2\backslash ),$ and $\backslash (\backslash$beta$=\backslash$gamma$=0\mathrm{.}1\backslash ).$

$($a$)$ Use the demand data from Days $2$ and $3$ to initialize Winter's method.

$($b$)$ What is your forecast for the total demand on Day $4?$

$($c$)$ Suppose the demand in the morning on Day $4$ turns out to be $27.$ What is your forecast for the total demand in the remainder of Day $4?$