LINEAR PROGRAMMING PROBLEMS: A PRACTICAL EXAMPLE AND OPTIMAL SOLUTION BASED ON THE SIMPLEX METHOD

Abstract

This article examines the theoretical and methodological foundations of solving linear programming problems using the simplex method. In the study, a multi-product production process was selected as a practical example, and a mathematical model was developed based on four types of products, several resource constraints, production capacity, and market demand. The model was solved step by step using the simplex method, and an optimal production plan was determined. According to the calculation results, the optimal solution is , , , and the maximum value of the objective function is equal to unity. The results confirm the practical importance of the simplex method in rational allocation of production resources, profit maximization, and scientific substantiation of management decisions.