$(60$ points$)$ Demand data for two years is provided below.

a$)$ Make initial estimates of level, slope, and seasonal factors.

b$)$ Use the $($Winter$\text{'}$s$)$ triple$-$exponential smoothing method to produce a forecast for each month in year $3$ from the end of year $2.$

c$)$ Produce a forecast for the remaining $11$ months of year $3$ after observing demand for the first month of year $3$ as $14.$ Use smoothing constants $=0\mathrm{.}2,=0\mathrm{.}1,=0\mathrm{.}1.$

$\backslash$table$[[$Month$,$Year $1,$Year $2],[$Jan$,15,16],[$Feb$,22,16],[$Mar$,40,45],[$Apr$,52,44],[$May$,76,86],[$Jun$,130,156],[$Jul$,110,130],[$Aug$,89,84],[$Sep$,67,55],[$Oct$,47,48],[$Nov$,19,15],[$Dec$,20,24]]$