A health Centre will be built to serve $7$ communities. The geographical location of the communities and their population is shown in the table below.

$$ Communities A$,$ X $=2\mathrm{.}5($km$),$ Y$=4\mathrm{.}5($km$),$ Population$(000\text{'}$s$)=2$

$$ Communities B$,$ X $=2\mathrm{.}5($km$),$ Y$=2\mathrm{.}5($km$),$ Population$(000\text{'}$s$)=5$

$$ Communities C$,$ X $=5\mathrm{.}5($km$),$ Y$=4\mathrm{.}5($km$),$ Population$(000\text{'}$s$)=10$

$$ Communities D$,$ X $=5($km$),$ Y$=2($km$),$ Population$(000\text{'}$s$)=7$

$$ Communities E$,$ X $=8($km$),$ Y$=5($km$),$ Population$(000\text{'}$s$)=10$

$$ Communities F$,$ X $=7($km$),$ Y$=2($km$),$ Population$(000\text{'}$s$)=20$

$$ Communities G$,$ X $=9($km$),$ Y$=2\mathrm{.}5($km$),$ Population$(000\text{'}$s$)=14$

There is a possibility of building the Centre in two communities, community C and F$.$ Based on the Demand$-$Distance criterion what is your recommendation for the site of the Centre. The distances to be measured based on Rectilinear method.

Based on the data in question and using the 'Centre of Gravity' which community is the most appropriate for the construction of the Centre?