Linear Programming In Operations Research In response to what is linear programming in operations research. It speak that this is a mathematical optimization method that allows. The representation of linear models to reduce costs or maximize profits in different areas of an organization or company. Are you interest in learning how linear programming works in this application area? Keep reading!
What Is Linear Programming In Operations Research
In other words, linear programming is a method through which an objective function is optimized, either by maximizing or minimizing said function, in which the variables are raised to power 1. This field of linear programming is an area of mathematical programming dedicated to maximizing or minimizing a linear function that receives the name of “objective function” so that the variables of such a function are subject to a series of restrictions expressed through a system of linear equations or inequalities.
When studying what linear programming is in operations research, it is essential to point out that it is application to the efficient administration of processes in many areas of the economy, as well as the knowledge that there is a diversity of software on the market. , which helps to represent the linear programming approach or model.
It is essential to consider that linear programming in operations research comprises two fundamental elements. The feasible region and the structural and non-negativity constraints.
The constraints are called non-negativity constraints and are known as model conditions stipulating that the decision variables must have only non-negative values, positive or null. The set of values that satisfy all the constraints is called the feasible region, which is classified as a solution space or all possible points of an optimize problem that help the problem’s constraints, including potentialities, equalities, and full restrictions.
Origin Of Linear Programming In Operations Research
Knowing what linear programming is in operations research implies delimiting that it does not come from computer programs
but its origin is a term of a military nature since programming means making proposals or time plans for training, logistics, or deployment of combat units.
Many consider that this term was uses by G. Monge in 1776. Still, the truth is that LV Kantorovich is consider as one of its creators. Since he presented it in his book on mathematical methods for organization and production.
Operations research and linear programming were boost with the appearance of computers. One of the most critical moments was the arrival of the simplex method.
The Simplex Method Linear Programming In Operations Research
When it comes to linear programming, it is also important to note that there is a method known as simplex method. Which comprises an analytical means of solving linear programming problems.
which is capable of solving models that are more complex than those that are solve uses the graphical method. With no restriction on the number of variables.
Types of Solutions in Linear Programming
Linear programs that have two variables are classified according to the type of solution they present and can be the following.
Affordable
When a set of solutions or values satisfies the constraints, they divide into single or multiple answers. Furthermore, an limitless solution establish.
In mathematical optimization, a feasible region or a feasible set is a search or solution space. That is, it is the set of all possible points of an optimization problem that satisfy the constraints of the problem.
Not Affordable
It happens when no set of solutions satisfies the constraints. That is when they are inconsistent.
Application Areas
To better understand what linear programming is in operations research. Its application areas takes into account since linear programming is an optimal solution tool that is apply in aspects related to efficient administration in all areas of the economy, so it is a common practice in.
Engineering area, because it allows the software to carry out computer programming tasks.
The scientific area allows the resolution of scientific problems with analysis, observation, and study through programming.
Since it is widely apply in the administrative, accounting, and economic regions to reduce costs or increase profits through functional models. The business area is commonly uses in the executive, accounting, and financial parts.
Linear programming is also uses in micro economics and business administration to increase the maximum income or minimize the costs of a production system.
Similarly, it is uses in marketing and advertising to identify the most feasible combination of media to advertise products. In this sense, you can start from a fixed budget for advertising so that the products reach a greater diffusion. In other cases, the restrictions indicate the available of each medium and give the advertising policies of the companies. If you want to know more about what linear programming is in operations research and its uses in algebra or its application to algorithms. Don’t forget that you can train at the best school specializing in economics, Euroinnova.
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Conclusion
In response to what linear programming is in operations research. It can be said that this is a mathematical optimization method that allows. The representation of linear models to reduce costs or maximize profits in different areas of an organization or company. The set of values that satisfy all the constraints is called the feasible region. Which is classified as a solution space or all possible points of an optimization problem that help the problem’s conditions. Including potentialities, equalities, and full restrictions.
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