Abstract
One of the pressing issues in the field of economic process automation is the complexity of finding an analytical solution to optimal control problems in nonlinear economic models. This is due to complex interdependencies between variables, constraints on resource allocation, and external influences. In such conditions, traditional analytical methods become ineffective, requiring the application of numerical algorithms. This paper presents a numerical algorithm for optimal resource allocation in an open economic system. The method is based on the use of Lagrange multipliers and the golden section method to determine the stationary state of the system under labor and investment resource constraints. The proposed approach automates computational processes and ensures high calculation accuracy. The mathematical package Maple was used to implement the algorithm. The paper discusses the features of the algorithm’s software implementation and provides numerical experiments demonstrating its stability and accuracy. The developed algorithm can be applied in resource management information systems, automated planning, and decision-making systems in enterprises. It enables modeling of economic processes and forecasting optimal resource allocation trajectories considering external factors. The obtained results confirm the effectiveness of the approach for automation and information technologies in economic analysis and management.