The demand forecast for Mthembu Enterprises indicates significant growth over the

next ten years and this requires the organization to build a new manufacturing facility.

There are three $(3)$ potential sites, namely, KwaZulu Natal, Gauteng and Eastern

Cape. The fixed and variable cost for each site is listed in the table below:

Potential Site Fixed Cost $($R$$s$)$ Variable Cost $($R$$s$)$

KwaZulu Natal $90000075$

Gauteng $150000055$

Eastern Cape $200000045$

$$ Solve for crossover point KwaZulu Natal and Gauteng.

$$ Solve for crossover point Gauteng and Eastern Cape.

$$ Evaluate the optimum number of products for each site. $(15)$

$2\mathrm{.}2$ The forecasting information for Siyafunda Trading is provided in the table below:

Month Actual Sales Units $$ Year $2022$

January $8025$

February $7650$

March $7950$

April $6655$

May $8452$

June $10890$

July $8665$

August $12775$

September $11980$

October $14760$

November $8730$

December $6950$

Calculate the $2023$ forecast for Siyafunda Trading using the exponential smoothing forecasting

technique with a smoothing constant of $0\mathrm{.}3$ and forecast for January $2022$ sales of $9525$ units.