Problem $18-7($Algo$)$

The following table contains the demand from the last $10$ months:

$\backslash$table$[[$MONTH$,\backslash$table$[[$ACTUAL$],[$DEMAND$]]],[1,33],[2,36],[3,37],[4,38],[5,42],[6,38],[7,41],[8,43],[9,40],[10,41]]$

a$.$ Calculate the single exponential smoothing forecast for these data using an $$ of $0\mathrm{.}20$ and an initial forecast $(F_1)$ of $33.$ Note: Round your answers to $2$ decimal places.

$\backslash$table$[[$Month$,\backslash$table$[[$Exponential$],[$Smoothing$]]],[1,33\mathrm{.}00],[2,33\mathrm{.}00],[3,33\mathrm{.}60],[4,34\mathrm{.}28],[5,35\mathrm{.}02],[6,36\mathrm{.}09],[7,36\mathrm{.}47],[8,37\mathrm{.}38],[9,38\mathrm{.}50],[10,38\mathrm{.}50]]$

b$.$ Calculate the exponential smoothing with trend forecast for these data using an $a$ of $0\mathrm{.}20,$ a $$ of $0\mathrm{.}20,$ an initial trend forecast $(T_1)$ of $1\mathrm{.}00,$ and an initial exponentially smoothed forecast $(F_1)$ of $32\mathrm{.}00.$

Note: Round your answers to $2$ decimal places.

$\backslash$table$[[$Month$,$FIT$],[1,0\mathrm{.}00],[2,3\mathrm{.}22],[3,3\mathrm{.}72],[4,4\mathrm{.}41],[5,8\mathrm{.}53],[6,6\mathrm{.}91],[7,5\mathrm{.}72],[8,7\mathrm{.}09],[9,5\mathrm{.}53],[10,6\mathrm{.}57]]$

c$-1.$ Calculate the mean absolute deviation $($MAD$)$ for the last nine months of forecasts.

Note: Round your answers to $2$ decimal places.

$\backslash$table$[[,$MAD$],[$Single exponential smoothing forecast,$],[$Exponential smoothing with trend forecast,$]]$

c$-1.$ Calculate the mean absolute deviation $($MAD$)$ for the last nine months of forecasts. Note: Round your answers to $2$ decimal places.

$\backslash$table$[[,$MAD$],[$Single exponential smoothing forecast,$],[$Exponential smoothing with trend forecast,$]]$

$c-2.$ Which is best?

Single exponential smoothing forecast

Exponential smoothing with trend forecast