The article covers the theoretical foundations and practical applications of the Simplex method used in solving linear programming problems. The Simplex method is defined as the process of finding an optimal solution that provides the maximum or minimum value of the objective function through successive approximations. The article describes in detail the two main stages of the method - finding an initial base solution and determining the optimal solution. The structure of the simplex table, algorithms for selecting the decisive element, column and row, as well as the table replacement process are explained. A step-by-step solution of the linear programming problem given as an example using the Simplex method is presented and the practical application of the method is demonstrated. The article serves as a useful resource for students and specialists working in the field of mathematical optimization.

Simplex method, linear programming, optimal solution, basic plan, Simplex table, decisive element, objective function, canonical form, free terms, iteration.

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