Abstract
The dynamic development of the global economy and the impact of external factors create challenges for ensuring sustainable growth, making effective resource management an urgent task. This paper addresses the problem of optimal resource management in an open economy model with constraints on labor distribution, investment, and foreign trade balances. To solve this problem, a numerical implementation algorithm based on a modified Lagrange multipliers method is proposed. The developed algorithm enables obtaining a numerical solution to the optimal control problem (OCP) and makes the model applicable for practical use. The conducted computational experiments confirmed the effectiveness of the approach: the constructed state and control trajectories demonstrate the achievement of a stable equilibrium state of the system while satisfying all imposed constraints. The practical value of the study lies in the fact that the algorithm provides the possibility of implementing numerical solutions to OCPs and using them for analyzing and forecasting economic development under resource limitations.