A chain of stores trading in a host of retail goods for urban customers is planning to set up operations in Manhattan. The exact location for the new outlet is to be decided. In order to do that, the company conducted a market survey and found five pockets of consumption in the city. The distance coordinates of these five pockets from a reference point in the grid map pertaining to the city are as follows: Zone $1(15,20),$ Zone $2(10,35),$ Zone $3(35,20),$ Zone $4(50,10),$ and Zone $5(40,20).$ The annual demand for the goods $($in tons$)$ in the five zones is $200,130,80,170,$ and $120,$ respectively.

$2\mathrm{.}1.$ What is the centre of gravity for setting up the operation in the city?