TN computer Services assembles customised personal computers from generic parts. Formed and operated by part time State University students Tyler and Becker, the company has steady growth since the time it started. The company assembles computers mostly at night $,$using part time students. Paulette and Maureen purchase generic computer parts in volume at a discount from variety of sources whenever they see a good deal $.$ Therefore $,$they need good forecast of demand for their computers so that they could know how many computer parts to purchase and store.

$($a$)$The company has accumulated the demand data shown in the below table for its computers for the past $12$ months, from which it wants to consider exponential smoothing forecasts using smoothing constants $(\backslash$alpha $)$ equal to $0\mathrm{.}30$ and $0\mathrm{.}50.$Create those forecasts for this company.

$($b$)$ Develop an adjusted exponentially smoothed forecast using the same $12$ months demand for this company $.$Do use the exponentially smoothed forecast with $(\backslash$alpha $)=0\mathrm{.}5$ with a smoothing constant for trend $\backslash$beta $,$ of $0\mathrm{.}30.$

$($c $)$ The demand data for TN Computer Services appears to follow an increasing linear trend. Do compute and draw a linear trend line for the company to see if it is more accurate than the exponential smoothing and adjusted smoothing forecasts developed in $($a$)$ and in $($b$)$ above.

Demand for Personal Computers for TN Computer Services

$1$ jan $37$

$2$ feb $40$

$3$ mar $41$

$4$ apr $37$

$5$ may $45$

$6$ jun $50$

$7$ jul $43$

$8$ aug $47$

$9$ sep $56$

$10$ oct $52$

$11$ nov $55$

$12$ dec $54$