Abstract. The paper presents the relevance of developing new methodological approaches for application of duality theory for more in-depth analysis of linear production planning problems. The theory of duality allows to find solutions to a dual problem in several ways, one of which is based on the construction of an inverse matrix. This matrix is obtained either from a simplex table involving the optimal plan or by algebraic methods from a matrix constructed on the basic vectors (corresponding variables are included in the basic of the optimal solution). In practice, finding an optimal solution to a linear programming problem by the iterative simplex method is a cumbersome process, the application of duality theory is possible only for problems in a small number of variables and constraints. In this paper we propose an algorithm that avoids routine calculations and finds an inverse matrix for further study of the production planning process. The algorithm is based on the reports of solving a linear programming problem built in MS Excel using the “Solver” add-in and the properties of the simplex method for solving linear programming problems. Studies have shown that this algorithm allows us to analyze the optimal production plan for linear problems in a large number of products, given production and demand constraints. The presented algorithm has a number of drawbacks, which in general do not significantly affect the process of finding the inverse matrix. Scientific research has shown that it is possible to further develop such methodological approaches to getting more complete information about the optimal solution of problems by the simplex method.