The spreadsheet $$forecasting$-$problem.xlsx$$ contains data for the past $30$ weeks of demand

for product X$.$ Based on the data, answer the following questions.

$($a$)$ Plot the data. Just by observing the plot, do you think a $3-$week simple moving average

would be a better forecast than a $6-$week simple moving average? Again, just by looking at

the plot, do you think an exponential smoothing with parameter $\backslash$alpha $=0\mathrm{.}2$ would be a better

forecast than an exponential smoothing with parameter $\backslash$alpha $=0\mathrm{.}6?$ Explain your reasoning.

$($For exponential smoothing, use $1=600$ for initialization of week $1.)$

$($b$)$ Out of the four possible forecasting models $(3-$week and $6-$week simple moving average

and exponential smoothing with parameters $\backslash$alpha $=0\mathrm{.}2$ and $\backslash$alpha $=0\mathrm{.}6),$ which is the best forecast?

Justify your answer by calculating the MAD. $($For exponential smoothing models, assume

the forecast for the first week is $600.)$ Here is the data set: $1574$

$21,004$

$3717$

$41,076$

$51,076$

$6932$

$71,291$

$81,219$

$9932$

$101,219$

$111,219$

$121,076$

$131,650$

$141,650$

$151,434$

$161,219$

$171,291$

$181,578$

$191,793$

$201,721$

$211,578$

$221,865$

$231,434$

$241,793$

$251,865$

$261,506$

$271,650$

$281,506$

$291,721$

$301,506$