$3.$ Consider the data for Problem $2.$

a$.$ Using the data from $2016$ and $2017,$ determine initial values of the base level, trend, and

seasonal factors for Winter$$s Method.

b$.$ Assume that the observed demand for the first quarter of $2018$ was $18.$ Using $\backslash$alpha $0\mathrm{.}2,$

$\backslash$beta $0\mathrm{.}15$ and $\backslash$gamma $0\mathrm{.}1,$ update the estimates of the base level at the first quarter of $2018,$

the trend, and the seasonal factors.

c$.$ What are the forecasts made at the end of the first quarter of $2018$ for the remaining three

quarters of $2018?$