The aim of this paper is to investigate the methods of linear programming and their application in economics. An important part and basis of understanding quantitative methods and the very concept of applying mathematics in business decision making is precisely linear programming. Linear programming deals with the optimization of given resources, either material (quantity of goods) or inmaterial (human resources) within given limits. It is a set of methods and procedures used to solve different theoretical and practical problems in different areas. In economics, it is used, for example, to minimize production costs, determine the maximum profit to determine the optimal distribution of labor, etc. The standard problem in linear programming is the maximum problem or the minimum problem. The paper analyzes the three most well - known methods for solving linear programming problems, namely the simplex method, the graphical method and the methods for solving the transport problem. The simplex method is a finite, iterative, and general method for solving linear programming problems. The graphical method is used to solve a problem that has only two variables. The advantage of this method is visualization that helps in easier understanding and problem solving. The paper describes the three most well-known methods for solving transport problems, namely the northwest angle method, the least squares method and the Vogel method. It is explained what these parameters are in order to use a particular method to solve a specific problem. All researched and written theory is supported by examples from practice. In the practical part of the paper, a concrete example is solved using Microsoft Excel Solver, which uses the simplex method to solve linear programming problems.