Question $4$: $(6$ marks$)$

The instant paper clip office supply company sells and delivers office supplies to companies, schools, and agencies within a $50-$ mile radius of its warehouse. The manager of the company wants to be certain that enough drivers and vehicles are available to deliver orders promptly and that they have adequate inventory in stock. Therefore, the manager wants to be able to forecast the demand for deliveries during the next month. From the records of previous orders, management has accumulated the following data for the past $9$ months.

$\backslash$table$[[$Month$,$Sales$],[$January$,65],[$February$,70],[$March$,80],[$April$,85],[$May$,90],[$June$,130],[$July$,155],[$August$,160],[$September$,190]]$

a$.$ Make forecasts for the sales using $4-$period moving average method. $(1\mathrm{.}5$ marks$)$

b$.$ Use the exponential smoothing method with $=0\mathrm{.}4$ as a smoothing constant to forecast the sales. Assume that the initial forecast for January is $60.(1\mathrm{.}5$ marks$)$

c$.$ Calculate the error and the absolute error for each forecast and summarize your computations in the table below. $(1$ mark$)$

d$.$ Compute the MAD as an accuracy measure for evaluating the performance of forecasting method then decide which forecasting method provides a better forecast? Explain your decision. $(1\mathrm{.}5$ marks$)$

e$.$ Use the better of the two methods $($MA$(4)$ or ES$(0\mathrm{.}4))$ to forecast sales for next October. $(0\mathrm{.}5$ mark$)$

$\backslash$table$[[$Month$,\backslash$table$[[$Sales$],[($Y$)]],4-$Month Moving Average $($F$),$Error,Absolute error,Square error, Exponential

Smoothing with

$=0\mathrm{.}4$

$(F),$Error,Absolute error,Square error$],[$January$,65,,,,,60,,,],[$February$,70,,,,,,,,],[$March$,80,,,,,,,,],[$April$,85,,,,,,,,],[$May$,90,,,,,,,,],[$June$,130,,,,,,,,],[$July$,155,,,,,,,,],[$August$,160,,,,,,,,],[$September$,190,,,,,,,,]]$