The article considers the task of building an effective and efficient organization of the management processes of a medical organization. A distinctive feature is noted - social orientation as the main function, and not just profit maximization with limited resources. This approach requires taking into account not only financial and resource components, but also the impact of many other external factors. However, the authors, realizing the difficulty of describing them, propose to take into account the effect of the "social orientation of the institution" in an implicit form when describing the financial condition of the organization. Taking into account implicit, including external, factors is possible when implementing models not only of statistical and financial analysis, as is usually accepted, but also their extensions to some image recognition methods, which often have a simple computer implementation. In particular, the formalization of the financial condition model of the organization is proposed, which reduces to the problem of mathematical programming with state vectors of both internal and external factors. The possibility of considering a decision-making model that would take into account the influence of possible external factors is also considered, while the "informality" of the problem in the sense of the absence of classical methods of solution is indicated. In this regard, it is proposed to reduce the model to the task of discriminant analysis, which is essentially a system of inequalities. Methods for solving systems of linear inequalities are known, but they are difficult to implement. For this reason, it is proposed to add an optimality criterion (objective function) to the discriminant analysis model, which allows to obtain a linear programming problem that already has simpler computer implementations of solutions. However, this possibility is present only in the case of linear constraints, which is a somewhat special case of the general problem. To solve the problem, in its broadest sense, it is proposed not only to reduce it to mathematical programming, and then to discriminant analysis, but also an effective recognition algorithm indicating the solvability of the problem. The process of constructive problem solving often requires a lot of time and effort, even with the powerful development of modern technologies. With the help of the given recognition algorithm, the discriminant analysis model in some formulation is output in a matrix form, which allows us to conclude when the model has the existence of a separating functional. The authors also propose the use of majority committee methods. The derived algorithm is quite simple to implement, but at the same time effective and efficient in practice, which makes it universal for this kind of tasks.