Facility location problem

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Find a location (say x-y coordinates) that minimizes a weighted sum of distances to each of several locations. An example is to locate a hospital or school to serve a community defined by population centers. Originally considered by Fermat in the 17th century, there are now many variations of this problem. One variation is the location of an obnoxious facility, such as a garbage dump. In that case the objective is to maximize total (weighted) distance from the given points (there are constraints, such as cost, that require the location to be within some distance of the points).

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