What is Linear Programming ?

By      17 - 24 July, 22
What is linear programming ?

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Linear programming is a strategy that assists us in determining the optimal solution for a given problem. An optimum solution is the best possible outcome of a given problem. In basic terms, it is the process of determining how to do something in the best possible way given limited resources. It is the strategy of maximizing resource utilization to get the greatest possible outcome for a certain purpose. Such criteria as lowest cost, biggest margin, or shortest time on such resources have other applications. Amendable programming analysis is used in situations where the optimal values of variables must be found while adhering to particular limitations. Calculus and marginal analysis are ineffective in dealing with these problems.

 

Linear Programming Problems

The following are the most important uses of linear programming which are used to solve Linear programming problems.

 

 

1. Manufacturing Problems

These issues are connected to issues in the industry, such as the need for some industries to produce a certain number of units of various products while requiring a set amount of labor, operating hours, and manpower per unit of product, among other things, in order to maximize profit from the sale of these products.

 

2. Diet Problems

In order to minimize costs and take into account food availability and costs, it is used to determine how much of various types of elements should be included in the diet.

 

3. Transportation Problems

 

The best strategy to deliver a product from factories or plants located in various places to markets is to identify the lowest transportation schedule possible.

 

Basic Terminologies used in Linear Programming Problems

 

Example of linear programming


You must have a firm understanding of the fundamental terminology utilized in solving linear programming problems in order to solve them. These terms are listed below:

 

  • Objective Function

The issue must have involved a problem with a distinct and definable aim, such as the maximization of profit or the reduction of costs, etc. These examples all come within the category of the objective function.

 

  • Decision Variable

Variables, like products and services, that are in competition with one another for a limited amount of resources. The term "decision variable" refers to a set of variables that are connected and have a linear connection that can determine the most ideal solution.

 

  • Constraints

The limitations placed on the available resources, such as a limited number of machinery, manpower, etc.

 

  • Redundant Constraints

Redundant restrictions are those that are clearly present and yet don't limit the solution to the problem being studied.

 

  • Optimum Solution

This is the finest option out of all the ones that could work to assist the problem's goal in the best way.

 

  • Feasible Solution

These are all feasible solutions that fulfil the constants and have the form of variables.

 

 

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