$27.$ For the data for problems $16$ through $21,$ use the arithmetic average of the first six months of data as a baseline to initialize the exponential smoothing.

a$.$ Determine the one$-$step$-$ahead exponential smoothing forecasts for August through December, assuming $\backslash (\backslash$alpha$=\backslash ).20.$

b$.$ Compare the accuracy of the forecasts obtained in part $($a$)$ with the one$-$step$-$ahead six$-$month moving$-$average forecasts determined in problem $20.$

c$.$ Comment on the reasons for the result you obtained in part $($b$).\backslash$begin$\{$tabular$\}\{|$l$|$r$|\}$

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

$\backslash$hline Jan & $89\backslash \backslash$

$\backslash$hline Feb & $57\backslash \backslash$

$\backslash$hline Mar & $144\backslash \backslash$

$\backslash$hline Apr & $221\backslash \backslash$

$\backslash$hline May & $177\backslash \backslash$

$\backslash$hline Jun & $280\backslash \backslash$

$\backslash$hline Jul & $223\backslash \backslash$

$\backslash$hline Aug & $286\backslash \backslash$

$\backslash$hline Sep & $212\backslash \backslash$

$\backslash$hline Oct & $275\backslash \backslash$

$\backslash$hline Nov & $188\backslash \backslash$

$\backslash$hline Dec & $312\backslash \backslash$

$\backslash$hline

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