Linear Programming

Linear programming is one of the most significant sections of mathematics, where the study of theoretical and methodological bases for solving specific problems is carried out. This mathematical discipline has been widely used in recent years in a variety of 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 devoted to numbers. This term was first proposed by T. Kupmans in 1951. The optimal plan for each linear program must be automatically linked with the optimal level of prices, that is, with objectively determined estimates.

Linear Programming: Methods

With the help of the linear programming technique , it is possible to solve a considerable number of extreme problems, which are connected with the economy. In this case, it is usually necessary 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 kind of programming is characterized by mathematical formulation of variables, sequence and a certain order of calculations, as well as logical analysis. This applies:

- if there is a mathematical certainty and quantitative limitations between the studied factors and variables;

- if there is an 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 helps to calculate the optimal performance of all machines, production lines, aggregates, as well as solving problems of rational use of available materials.

In agriculture, this method is used to determine the minimum cost of a feed allowance, taking into account the available amount of feed. This takes into account the types and content of certain useful substances in them.

In the foundry industry, this technique allows us to find a solution to the transport problem and the problems of the 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 the enterprises that are engaged in the production of products.

Linear Programming: Tasks

A distinctive feature of all economic problems, which are solved through the linear programming methodology, is the selection of certain solutions, as well as limiting conditions. Thanks to the solution of this problem, it is possible to find the optimal solution from all alternative variants.

Significant value in using the methodology of linear programming in the economy is the choice of the most optimal variant from a large number of all options that are considered acceptable. It is almost impossible to solve such tasks in other ways, since only they allow to find the degree of rationality of the use of production resources. With the help of linear programming, the main task is solved, such as transportation, which should minimize the turnover of consumer goods in the process of their delivery from the manufacturer.

Linear Programming in Excel

In the process of solving such problems, it is necessary to first form a model, which implies the formulation of conditions in the mathematical language. After this step, you can find a solution through a graphical method. To do this, Excel has a special "Find Solution" function.

As already clear from the above, linear programming has a very wide scope.