Use the data set below to answer the questions that follow. $($Show your work for maximum credit$)$

$$

Period$$ Demand Sales Volume

$11000$

$21200$

$31450$

$41700$

$51850$

$61950$

$$

a$.$ Find the four$-$period simple moving average forecasts for Periods $5$ and $6.$

b$.$ Find the four$-$period weighted moving average forecasts for Periods $5$ and $6$ using weights of $0\mathrm{.}05,0\mathrm{.}25,0\mathrm{.}30,$ and $0\mathrm{.}40$ from the earliest period to the latest period, respectively.

c$.$ Which set of forecasts is more accurate, the simple moving average forecasts or the weighted moving average forecasts? Why is that set of forecasts more accurate in this particular case?

d$.$ Will that type of forecast always be more accurate? Why or why not?