$4.$ Beth's Hot Chips on$-$line business uses a T$1$ line to connect their electronic business to the internet. They have been in business for one year and have had the same bandwidth $($Internet access capacity$)$ for that entire year. Their percentage utilization is given as follows:

Month Bandwidth

January $35\mathrm{.}5\%$

February $38\mathrm{.}2\%$

March $44\mathrm{.}1\%$

April $47\mathrm{.}7\%$

May $51\mathrm{.}2\%$

June $55\mathrm{.}9\%$

July $60\mathrm{.}0\%$

August $62\mathrm{.}3\%$

September $65\mathrm{.}7\%$

October $71\mathrm{.}1\%$

November $75\mathrm{.}7\%$

December $79\mathrm{.}3\%$

Produce a forecast for the next month $($January of next year$)$ using each of the following techniques:

a$)$ Three period moving average.

$(71\mathrm{.}1+75\mathrm{.}7+79\mathrm{.}3)/3=75\mathrm{.}37\%$

b$)$ Three period weighted moving average using the weights of $1,2,$ and $5.$

$(71\mathrm{.}1+151\mathrm{.}4+396\mathrm{.}5)/8=77\mathrm{.}375\%$

c$)$ Exponential smoothing using the forecast for the first period of $35\%$ and $=0\mathrm{.}8.$

From data analysis using exponential smoothing tool, the forecast is $78\mathrm{.}36\%$

d$)$ Linear trend model.

Y$=3\mathrm{.}971$x$+31\mathrm{.}413$

Y$13=3\mathrm{.}971(13)+31\mathrm{.}43$

Y$=83\mathrm{.}03\%$

e$)$ What would you recommend to Beth regarding the forecast for the next month? Explain.

f$)$ Based on the analysis, estimate when will Beth need additional bandwidth?