Abstract
This paper is devoted to the study of efficient resource allocation in an open three-sector economy model, taking into account external and internal constraints. The aim of the study is to develop an algorithm for finding a steady state of the economic system and efficient allocation of labor and investment resources. The model is based on the Cobb-Douglas production functions, which describe output depending on capital and labor. The main attention is paid to issues of resource allocation, investment and compliance with balance equations. The use of the Lagrange multiplier method to maximize production in the consumer sector made it possible to determine the efficient values of the control parameters, which contributes to achieving sustainable balanced growth and equilibrium in the economic system. The scientific significance of the study lies in expanding the understanding of stable states of open three-sector economic models, which contributes to improving the allocation of resources in production systems. The article discusses existing analysis methods and algorithms with an emphasis on mathematical modeling and numerical methods for solving nonlinear programming problems. Algorithmic and software aspects of economic system modeling are also described, including software implementation in the Maple language. The work emphasizes the importance of scientific and technological progress and efficient resource allocation to achieve economic development goals