Linear programming is one of the most significant branches of mathematics, where the theoretical and methodological foundations of solving certain problems are studied. This mathematical discipline has been widely used in recent years in various economic and technical fields, where not the last role is assigned to mathematical planning and the use of automatic calculation systems. This section of science is devoted to the study of linear optimization models. That is, linear programming is dedicated to numbers. This term was first proposed by T. Coopmans in 1951. The optimal plan of each linear program must be automatically associated with the optimal price level, that is, with objectively determined estimates.
Linear programming: methods
Using the linear programming technique , it is possible to solve a considerable number of extreme problems that are associated with the economy. In this case, it is usually required to find the extreme values of some functions of a variable. As the basis of linear programming, the solution of a system of linear equations that are transformed into equations and inequalities is expressed. This type of programming is characterized by the mathematical formulation of variables, the sequence and a certain order of calculations, as well as logical analysis. This applies:
- if there is mathematical certainty and quantitative limitedness between the studied factors and variables;
- if there is interchangeability of factors due to the sequence of calculations;
- if mathematical logic is combined with an understanding of the essence of the phenomena that are being studied.
Linear programming in industrial production contributes to calculating the optimal performance of all machines, production lines, units, as well as solving the problems of rational use of available materials.
In agriculture, using this method, the minimum cost of the feeding ration is determined taking into account the available amount of feed. In this case, the types and content of certain useful substances in them are taken into account.
In foundry, this technique allows you to find a solution to the transport problem and the problem of mixtures that are part of the metallurgical charge. The essence of the transport task in this case implies the optimal attachment of consuming enterprises to enterprises engaged in the production of products.
Linear programming: tasks
A distinctive feature of all economic problems that are solved by linear programming techniques is the choice of certain solution options, as well as limiting conditions. Thanks to the solution of such a problem, it is possible to find the optimal solution from all alternative options.
A significant value in using the linear programming technique in economics is the choice of the most optimal option from a large number of all options that are considered acceptable. It is almost impossible to solve such problems in other ways, since only they allow you to find the degree of rationality of the use of production resources. With the help of linear programming, such a basic problem as transport is solved, which should minimize the freight turnover of consumer goods in the process of their delivery from the manufacturer.
Linear programming in Excel
In the process of solving such problems, for starters, it is necessary to create a model, which implies the formulation of conditions in a mathematical language. After this stage, you can find a solution using the graphical method. To do this, Excel has a special function called “Solution Search”.
As already clear from the above, linear programming has a very extensive scope.