QUESTION $3$

$(20$ Marks$)$

EconoX is a leading manufacturing organization specializing in the production of environmentally sustainable products. Founded in $2005,$ 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 of $154$ items in the most recent period completed, a forecast of $172$ items for that period, and a smoothing constant of $0\mathrm{.}3.$ On the other hand, the operations manager utilizes trend projection in predicting quarterly demand for electric vehicle washers using the equation $\backslash ($ y $\backslash )-$hat $\backslash (=250-2\mathrm{.}5$ x $\backslash ),$ where $\backslash ($ x$=1\backslash )$ in 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.

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|\}$

$\backslash$hline SEGMENT & $\backslash$begin$\{$tabular$\}\{$c$\}$

MARKETING $\backslash \backslash$

R$($thousands$)$

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

SALES $\backslash \backslash$

R$($thousands$)$

$\backslash$end$\{$tabular$\}\backslash \backslash$

$\backslash$hline $1$ & $14$ & $6\backslash \backslash$

$\backslash$hline $2$ & $11$ & $3\backslash \backslash$

$\backslash$hline $3$ & $15$ & $5\backslash \backslash$

$\backslash$hline $4$ & $16$ & $5\backslash \backslash$

$\backslash$hline $5$ & $24$ & $15\backslash \backslash$

$\backslash$hline $6$ & $28$ & $18\backslash \backslash$

$\backslash$hline $7$ & $22$ & $17\backslash \backslash$

$\backslash$hline $8$ & $21$ & $12\backslash \backslash$

$\backslash$hline $10$ & $26$ & $14\backslash \backslash$

$\backslash$hline $11$ & $43$ & $5\backslash \backslash$

$\backslash$hline $12$ & $34$ & $14\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

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

$\backslash ((6\backslash )$

how this would change if the smoothing constant were adjusted to $0\mathrm{.}6.$

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 $\backslash (1=1\mathrm{.}5\backslash )$; Quarter $2\backslash (=0\mathrm{.}8\backslash )$;

$\backslash ((4\backslash )$

Quarter $3=1\mathrm{.}1$; and Quarter $\backslash (4=0\mathrm{.}6\backslash ).$

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$)$