Problem $3-7($Algo$)$

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

$\backslash$table$[[$MONTH$,$ACTUAL DEMAND$],[1,31],[2,33],[3,34],[4,42],[5,45],[6,44],[7,42],[8,44],[9,41],[10,43]]$

a$.$ Calculate the single exponential smoothing forecast for these data using an $$ of $0\mathrm{.}40$ and an initial forecast $(F_1)$ of $31.$ Note: Round your intermediate calculations and answers to $2$ decimal places.

$\backslash$table$[[$Month$,\backslash$table$[[$Exponential$],[$Smoothing$]]],[1,],[2,],[3,],[4,],[5,],[6,],[7,],[8,]]$

a$.$ Calculate the single exponential smoothing forecast for these data using an $$ of $0\mathrm{.}40$ and an initial forecast $(F_1)$ of $31.$

Note: Round your intermediate calculations and answers to $2$ decimal places.

$\backslash$table$[[$Month$,\backslash$table$[[$Exponential$],[$Smoothing$]]],[1,],[2,],[3,],[4,],[5,],[6,],[7,],[8,],[9,],[10,]]$

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

Note: Round your intermediate calculations and 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