Linear programming is a mathematical technique.
The mathematical technique that allows the optimization of an objective function through the application of various restrictions to its variables is known as linear programming . It is a model composed, therefore, of an objective function and its restrictions, all of these components being constituted as linear functions in the variables in question.
Throughout history there have been several important events related to linear programming, such as these:
-During World War II it was kept secret and was used as a mechanism to manage and plan all expenses. In this way, the aim was to better manage our own resources and reduce the army's costs as much as possible.
-Three are considered its fathers or creators: the Hungarian-American John von Neumann, the American professor George Dantzig and the Russian-born mathematician Leonid Kantorovich, who received the Nobel Prize in Economics in 1975.
Linear programming models
Linear programming models contemplate that the decision variables (that is, the objective function and the restrictions) maintain linear behavior. This means that, through its method , the calculations can be simplified and a result close to reality can be obtained.
In addition to everything stated above, we cannot ignore the existence of another important series of concepts that are related to the aforementioned linear programming. In this case, we are referring to three in particular:
-Feasible solution. Under this name there is an enclosure, which may or may not be bounded and which is determined by what is the set of restrictions of all the semiplanes. It is also known by the name of validity region.
-Optimal solution. This is what is called what is the set of all the vertices of the enclosure. It must also be emphasized that, specifically, this can be minimum or maximum depending on each case.
-Value of the linear program. In this case, this is the value that the aforementioned objective function takes at what is the vertex of the optimal solution.
Linear programming applies constraints to the variables of an objective function to optimize it.
An example
Let's look at an example of linear programming to better understand this definition. Suppose a man receives an inheritance of 100,000 pesos and makes the decision to invest the money . His accountant recommends two investments: buy shares in an oil company, which have a yield of 5% , and purchase government bonds , which yield 9% .
The man decides to invest no more than 80,000 pesos in oil stocks and no less than 15,000 pesos in state bonds. On the other hand, it aims that investment in stocks never doubles investment in bonds. Thanks to linear programming, you can estimate how to distribute your money between both options so that your investments offer you the greatest benefit.
The amount to invest in stocks can be named as X , while the amount to invest in bonds can be named as Y. The restrictions, on the other hand, will be that X cannot have a value greater than 80,000 , that Y cannot have a value less than 15,000 and that X+Y cannot exceed the value of 100,000 .
If these variables are transferred to a table or graph , it will be possible to know which are the most profitable options for the individual.