  We consider the stationary problem for a diffusive logistic equation with the
homogeneous Dirichlet boundary condition. Concerning the corresponding Neumann
problem, Wei-Ming Ni proposed a question as follows: Maximizing the ratio of
the total masses of species to resources. For this question, Bai, He and Li
showed that the supremum of the ratio is 3 in the one dimensional case, and the
author and Kuto showed that the supremum is infinity in the multi-dimensional
ball. In this paper, we show the same results still hold true for the Dirichlet
problem. Our proof is based on the sub-super solution method and needs more
delicate calculation because of the range of the diffusion rate for the
existence of the solution.
