Problems of modeling the production sphere of an enterprise with a nonlinear function «output-costs»

Traditional economic theory for the simplification purpose is limited by the analysis of an enterprise produced a single product, whereas in the reality enterprises can produce several varieties of a single product. Financial results of an enterprise, rates of enlarged reproduction, and its financial status depend on the level of costs and production. Technical and economic factors of production have a significant impact on the cost level. This influence is manifested depending on changes in equipment, technology, organization of production, in the structure and quality of products and the amount of costs for its production. The largest effect with limited costs depends on how the company solves the problems of balancing costs and output. The research paper covers theoretical aspects of costs and production of a multi-product enterprise, formulated as a problem of minimizing a convex function taking into account the limitations also set by convex numbers. The Kuhn-Tucker theorem is used to solve this problem. Differences between the theories of costs and production (output) for mono - and multi-product enterprises are revealed. The solution of the problem indicates that the optimal conditions for a multi-profile enterprise differ from those for enterprises with a single product. These differences are briefly discussed in the final section of the paper.