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The term 'linear programming' consists of two words: linear+programming. Linear Programming is widely used in Mathematics and some other fields such as economics, business, telecommunication, manufacturing, etc. The word 'linear' defines the relationship between multiple variables with degree one and the word 'programming' defines the process of selecting the best solution from various alternatives.
LP Problems in maths is a system process of finding a maximum or minimum value of any variable in a function, LP Problems is also known by the name of the optimization problem. A linear programming problem is helpful in developing and solving a decision-making problem by mathematical techniques. The problem is generally given in a linear function that needs to be optimised subject to a set of different constraints. The major usage of linear programming problems is in advising the management to make the most efficient & effective use of the scarce resources.
Different Parts of the linear programming problem Model:
Variables that are changeable, such as the profit function is affected by both sales and price, now which one of these two is changeable, will be our decision variable.
A linear function of the objective, either to Maximise or minimise. such as Maximise Profit as sales, production, etc, and Minimise Cost as Loss, energy, consumption, wastage, etc.
Any kind of limitation explained through a function like Limitations of raw materials, time, funds, equipment, etc.
The first one is Decision variables represent quantities whose determination has to take place. The second one is the objective function that shows how the decision variables will impact the cost or value whose optimization has to take place. The third one is Constraints explain how the decision variables utilize resources that are limited and the fourth one is Data quantifies the relationships that are represented in the constraints and the objective function.
Also, there are different types of linear programming such as Solving linear programming by Simplex method, Solving linear programming using R, Solving linear programming by graphical method, and Solving LP with the use of an open solver. There are some advantages and uses of linear programming such as Linear programming provides insights into business problems, It helps to solve multi-dimensional problems, According to change of the conditions, linear programming helps us in adjustments, By calculating the profit and cost of different things, LP also helps to take the best solution.
A linear programming problem should have a Well-Defined objective function to optimise which may be either to maximise contribution by utilizing available resources, or it may be to produce at the lowest value by using a limited amount of productive factors.
There must be a presence of constraints or restrictions on the use of limited resources which are to be allocated among various competitive activities.
There should be alternative courses of action. For example, it must be possible to make a selection between various additions of the productive factors such as men, machines, materials, market-etc.
All decision variables must be assumed as non-negative values because the negative value of physical quantities is an impossible situation.
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