We consider in this paper a method for solution of "inverse" problems of atmospheric admixture dispersal. It is based on solution of the adjoint semispherical equation of turbulent diffusion, as well as on dual representation of the functional of the admixture concentration. It is shown that this classical method can be generalized to the class of problems involving calculation of statistical characteristics of the admixture concentration. As an example, we consider the problem of how a plant with known pollution emission rate can be placed optimally, i.e., in such a way that the admixture concentration at a given location does not exceed the preset threshold within the preset probability limits.