Linear programming is actually the most important and most used technique of operational research, which has a very significant application primarily in economics, but also in other areas such as agriculture, industry, transport etc.. Linear programming with the support of mathematical models solves the problem and finds the optimal solution that is the result of rationally used resources. In this way, the company can achieve a minimum cost and maximum profit. The mentioned mathematical models first need to be defined and set, and this includes analyzing the goal function, decision variables and individual constraints. The mathematical models described in this final paper are: production model, food model, transport model and division of labor model, which is also called assignment. The assignment is part of the transport model, and describes the process of optimal distribution of jobs among workers, with one worker doing one job. The solving methods are: simplex method and graphical method. The simplex method uses an iteration mechanism to find the solution, while the solution the graphical method can be read from the graph. In addition, software such as Solver (as part of Excel) can be used to solve the problem of linear programming and systems of linear non-equations. This final paper constructs a solution to the problem of division of labor with the help of Solver (in Excel) and a solution of the graphical method for the production model. Finally, the most common application of linear programming in economics is listed.