$12\mathrm{.}2.$ The manager of the I$-85$ Carpet Outlet needs to be able to forecast accurately the demand for Soft Shag carpet $($its biggest seller$).$ If the manager does not order enough carpet from the carpet mill, customers will buy their carpets from one of the outlet's many competitors. The manager has collected the following demand data for the past eight months:

$\backslash$table$[[$Month$,\backslash$table$[[$Demand for Soft Shag$],[$Carpet $(1000$ yd$)]]],[1,5],[2,10],[3,6],[4,8],[5,14],[6,10],[7,9],[8,12]]$

a$.$ Compute a three$-$month moving average forecast for months $4$ through $9.$

b$.$ Compute a weighted three$-$month moving average forecast for months $4$ through $9.$ Assign weights of $\mathrm{.}55,\mathrm{.}33,$ and $\mathrm{.}12$ to the months in sequence, starting with the most recent month.

c$.$ Compare the two forecasts using MAD. Which forecast appears to be more accurate?