Three towns have decided that they would like to build jointly an airport to serve all thr...

Three towns have decided that they would like to build jointly an airport to serve all three communities. They also decided that the location of the airport should minimize the sum of the population-weighted, squared distance from the airport to each of the towns.

On a map coordinates (x, y) (from an arbitrary origin) of the towns are (2, 6), (7, 5), and (3, 1) with respective population of 60, 00, 30, 00, and 90, 00 people. Find the best location (x, y) for the airport, recalling that distance from point i to point j is

Verify the type of point found.