Problem $1(15$ points$)($Solve using Excel$)$

Eastport Manufacturing Company has demand for excavators over the period $2004$ to $2010$ as shown in the table below.

$\backslash$table$[[$Year$,$Demand$],[2004,74],[2005,79],[2006,80],[2007,90],[2008,105],[2009,142],[2010,122]]$

a$.$ Use the trend$-$adjusted exponential smoothing method to forecast the demand for year $2005$ through $2011.$ Assume that $F_1=74$ and $T_1=0$ and use $=0\mathrm{.}3$ and $=0\mathrm{.}4$ for the smoothing constants.

b$.$ Develop a trend line using the data in the table. Use this to predict the demand in year $2011.$ Show your detailed calculation of the trend line equation including calculations for the slope and the intercept.

c$.$ Which of the two forecasts is more accurate in terms of MAD and MAP,E$?$

d$.$ Develop a tracking signal for the trend line forecast and see if it stays within acceptable limits$,$ which we define as $3$ MADs. Why we use a tracking signal and what does it mean when a tracking signal exceeds the set limits$?$