Linear programming

Linear programming represents one of the most important branches of mathematics, where the study of theoretical and methodical bases of the solution of certain tasks. This mathematical discipline widely used in recent years in various economic and technical fields, where not last role is assigned to mathematics planning and use of automatic computing systems. This section of science devoted to the study of linear optimization models. That is, linear programming is devoted to numbers. For the first time this term was proposed by T. Koopmans in 1951. The optimal plan for every linear program it is necessary to automatically associate with optimum price level, that is, objectively conditioned estimates.

Linear programming: methods

With the help of methods of linear programming can solve a considerable number of extremal problems associated with the economy. In this case, is usually required to find the extreme values of certain functions of a variable. As the basis of linear programming is expressed the solution to system of linear equations that can be converted into equations and inequalities. This type of programming is characterized by a mathematical formulation of variables, sequence and specific order of the calculations and logical analysis. Applicable:

- if there is a mathematical certainty and quantitative constraints between the studied factors and variables.

- if there is interchangeability of factors, through a series of calculation;

- if mathematical logic combined with the understanding of the essence of the phenomena that are studied.

Linear programming in industrial production contributes to the calculation of the optimal performance of all machines, production lines, units, and solving problems of rational use of existing materials.

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In agriculture using this method is determined by the minimum value of the diet feeding given the available amount of feed. This takes into account the types and contents of specific nutrients.

In foundry this method allows to find solution of the transport problem and the problem of mixtures, which are part of the metallurgical charge. The essence of the transport problem in this case involves optimal attachment to the consuming enterprises to enterprises that are engaged in the production of products.

Linear programming: tasks

A Distinctive feature of all economic problems solved by methods linear programming is the choice of a certain solution, as well as limiting conditions. Thanks to the solution of this problem is possible to find the optimal solution from all the alternatives.

The Significant value of using the technique of linear programming in Economics is the choice of the optimal variant from a large number of all options that are considered valid possible. Such problems almost impossible to solve in other ways, as only they allow to find the extent of rational use of production resources. Using linear programming allowed such a basic task as transport, which should minimise the turnover of consumer goods in the process of delivery from the manufacturer.

Linear programming in Excel

In the process of solving such problems first we need to create a model that assumes the formulation of conditions in mathematical language. After this stage a solution can be found using a graphical method. To do this, in Excel there is a function called "Finding solutions".

As is clear from the above, linear programming has a very vast scope of application.