Mathematical Models and Economic Analysis of Linear Programming Problems

The article studies the role and importance of linear programming theory in solving problems of optimizing economic processes. The object of research is the problem of effective planning of production in conditions of limited resources. The article analyzes mathematical models of linear programming problems, the economic content of the objective function, and methods for forming a system of constraints. Also, the relationship between primal and dual problems is theoretically and practically substantiated.
The work presents the problem of optimal production planning based on a specific economic example, and its mathematical model is built. The range of possible solutions is determined, and the optimal solution is found using the geometric method. The results obtained are verified in the Python environment using the Simplex algorithm, and it is proven that they fully correspond to the solution using the graphical method. The results show that linear programming methods are an important tool for improving the efficiency of economic analysis, rational use of resources, and decision-making. The results of the study can be used in production management, economic planning, and optimal decision-making processes.