$[20$ points$]$ Donut King tracked sales for $2$ weeks. Sales data is in the following table.

Day Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su

Sales $157234132219171268177250249212246239289267$

a$.$ Develop a $3-$day moving average forecast for days $5-14$ and compute the MAD.

b$.$ Develop a $4-$day moving average forecast for days $5-14$ and compute the MAD.

c$.$ Develop forecast for days $5-14$ with a $3-$day weighted moving average in which sales for

the most recent day are given a weight of $3$ and sales in the previous $2$ days are given a

weight of $2$ and $1.($Wt$-1=3,$ Wt$-2=2,$ Wt$-3=1).$ What is the MAD?

d$.$ Which forecasting model is most accurate as per MAD values?

e$.$ Discuss whether MAD is a good tool to compare forecasting models or not.