Problem III $(10$ Points$)$

The Hartley$-$Davis motorcycle dealer in the Minneapolis$-$St$.$ Paul area wants to be able to forecast accurately the demand for the Roadhog Super motorcycle during the next month. From sales records, the dealer has accumulated the$-$ data in the following table for the past year.

$\backslash$begin$\{$tabular$\}\{|$l$|$c$|\}$

$\backslash$hline Month & Demand $\backslash \backslash$

$\backslash$hline January & $9\backslash \backslash$

$\backslash$hline February & $7\backslash \backslash$

$\backslash$hline March & $10\backslash \backslash$

$\backslash$hline April & $8\backslash \backslash$

$\backslash$hline Mai & $7\backslash \backslash$

$\backslash$hline June & $12\backslash \backslash$

$\backslash$hline July & $10\backslash \backslash$

$\backslash$hline August & $11\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

A$.$ Compute a three$-$month moving average forecast of demand for April through September

B$.$ Compute the forecast for September using the exponential smoothing technique, considering alpha $\backslash (=0\mathrm{.}3\backslash ).$

C$.$ Determine which on the two methods is the most precise one.

$\backslash$begin$\{$tabular$\}\{|$l$|$c$|$l$|$l$|$l$|$l$|\}$

$\backslash$hline Month & Demand & & & & $\backslash \backslash$

$\backslash$hline January & $9$ & & & & $\backslash \backslash$

$\backslash$hline February & $7$ & & & & $\backslash \backslash$

$\backslash$hline March & $10$ & & & & $\backslash \backslash$

$\backslash$hline April & $8$ & & & & $\backslash \backslash$

$\backslash$hline Mai & $7$ & & & & $\backslash \backslash$

$\backslash$hline June & $12$ & & & & $\backslash \backslash$

$\backslash$hline July & $10$ & & & & $\backslash \backslash$

$\backslash$hline August & $11$ & & & & $\backslash \backslash$

$\backslash$hline September & & & & & $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$