$25\%$QUESTION $3(20$ Marks$)$

EconoX $is$ a leading manufacturing organization specializing $in$ the production $of$ environmentally sustainable products.

Founded $in2005,$ the company has grown $to$ become a pioneer $in$ green manufacturing practices, producing a range $of$ ecofriendly

products including solar panels, energy$-$efficient home appliances, and electric vehicle components. One $of$ the

business analysts has applied the exponential smoothing technique $to$ predict solar panel returns $at$ one $of$ the branches $in$

Orania. Given $an$ actual number $of$ returns $of154$ items $in$ the most recent period completed, a forecast $of172$ items for that

period, and a smoothing constant $of0\mathrm{.}3.On$ the other hand, the operations manager utilizes trend projection $in$ predicting

quarterly demand for electric vehicle washers using the equation $y-$hat $=250-2\mathrm{.}5x,$ where $x=1in$ the first quarter. This $is$

$to$ enable the organization $to$ prepare for any changes $in$ capacity among others. Lastly the operations manager has

indicated that the organization has made significant inroads into the Southern African market, the sales volumes and

marketing expenses are provided below for the different geographical market segments.

SEGMENT

MARKETING

$R(thousands)$

SALES

$R(thousands)$

$1146$

$2113$

$3155$

$4165$

$52415$

$62818$

$72217$

$82112$

$92615$

$104320$

$113414$

$1295$

$3\mathrm{.}1$ Using the provided information, determine the forecast $of$ solar panels for the next period and demonstrate

how this would change $if$ the smoothing constant were adjusted $to0\mathrm{.}6.$

$(6$

marks$)$

Explain the difference $in$ terms $of$ alpha and responsiveness.

$3\mathrm{.}2$ Given that for electric vehicle washers the seasonal $(quarterly)$ indices are Quarter $1=1\mathrm{.}5$ Quarter $2=0\mathrm{.}8$

Quarter $3=1\mathrm{.}1$ and Quarter $4=0\mathrm{.}6.$

$(4$

marks$)$

Calculate the seasonally adjusted forecast for the electric vehicle washers for Quarters $5-8?$

$3\mathrm{.}3$ Using the provided information calculate a regression line for the data provided.

$(10$

marks$)$