Asymptotic optimal location of facilities in a competition between population and industries

We consider the problem of optimally locating a given number $k$ of points in ${\mathbb R}^n$ for an integral cost function which takes into account two measures $φ^+$ and $φ^-$. The points represent for example new industrial facilities that have to be located, the measure $φ^+$ representing in this case already existing industries that want to be close to the new ones, and $φ^-$ representing private citizens who want to stay far away. The asymptotic analysis as $k\to\infty$ is performed, providing the asymptotic density of optimal locations.

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