$(11$ marks: $1,1,1,1,1,3,3)$

$2.$ The usage of item #$14-46-506$: $4ft.$ Supersaver fluorescent lamps in the maintenance storeroom of ERCO Worldwide in Saskatoon in the first ten months of a given year are displayed below.

Fit a model to the data using each of the following techniques and forecast the November usage in each case. $($Show your work in the tables below$)$

a$.$ Three$-$month moving average.

b$.$ Five$-$month moving average.

c$.$ Exponential smoothing with smoothing constant $=0\mathrm{.}1.($Start with $10$ units as forecast for Feb.$)$

d$.$ Exponential smoothing with smoothing constant $=0\mathrm{.}3.($Start with $10$ units as forecast for Feb.$)$

e$.$ Linear trend $($regression$).$

f$.$ plot the two moving average forecasts and the actual $($in one graph$)($in Excel$),$ the two exponential smoothing forecasts and the actual $($in one graph$),$ and the linear trend and the actual $($in one graph$)($three graphs altogether. Plot the graphs in Excel and then copy and paste them into this Word document.$)$

Just by observing the plots, which of the above techniques would you use to forecast the usage of fluorescent lamps and why? $($Hint: The plot overall closest to actual demand will be most accurate.$)$

g$.$ Alternatively, compute the MAD for each forecasting technique and determine the most accurate technique.