  Consider a species whose population density solves the steady diffusive
logistic equation in a heterogeneous environment modeled with the help of a
spatially non constant coefficient standing for a resources distribution in a
given box. We look at maximizing the total population size with respect to
resources distribution, under some biologically relevant constraints. Assuming
that the diffusion rate of the species is large enough, we prove that any
optimal configuration is the characteristic function of a domain standing for
the resources location. Moreover, we highlight that optimal configurations look
{\it concentrated} whenever the diffusion rate is large enough. In the
one-dimensional case, this problem is deeply analyzed, and for large diffusion
rates, all optimal configurations are exhibited.
