$1.$ The healthcare facility is targeted to serve seven census tracts in Bangalore. The table given below shows the coordinates for the centre of each census tract, along with the projected populations, measured in thousands. Customers will travel from the seven census tract centres to the new facility when they need healthcare. Two locations being considered for the new facility are at $(5\mathrm{.}5,4\mathrm{.}5)$ and $(7,2),$ which are the centres of census tracts C and F$.$ Details of seven census tract centres, coordinate distances along with the population for each centre are given below. Find the target area$$s centre of gravity for the Health$-$care medical facility. $(10$ marks$)$