Problem $2(20$ points$).$ Monthly data for the sales of certain product at a local company during the las $9$ periods are shown in below table. $($Fill all the blanks. Allow $2$ decimal values$).$

$\backslash$table$[[$Month$,$Sales,MAF $(3),$Error,MAF $(6),$Error$],[1,1500,,,,],[2,1550,,,,],[3,1600,,,,],[4,1250,,,,],[5,1300,,,,],[6,1400,,,,],[7,1395,,,,],[8,1458,,,,],[9,1350,,,,]]$

a$.(5$ points$).$ Determine the forecasts for periods $5$ through $9$ using three$-$period moving averages, and the forecasts for periods $7$ and $9$ using six$-$month period moving averages.

b$.(5$ points$).$ Calculate the forecast errors for three$-$period moving averages and forecast errors for six$-$period moving averages.

c$.(5$ points$).$ Calculate the MAD for three$-$period moving averages and six$-$period moving averages.

d$.(5$ points$).$ If a smoothing constant of $0\mathrm{.}4$ was analyzed for the data, and you were informed that forecast for period $1$ was $1,450$; based on these assumptions, calculate the forecast for period $2.$