In a certain area there are N villages, and j'th village requires M(j) phone lines. Cost of a line is $1 per 1 km. Where should a phone company locate a (unique) station to cover the demand at the minimum cost?
Formulation:
There are m points A1,...,Am on the 2D plane. The problem is to minimize the weighted sum:
W1*|X-A1| + ... + Wm*|X-Am|
of the Euclidean distances from the design point X to the given points Ai.
Wi are user-set nonnegative weights.