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Table of Contents

What Is Linear Programming?

Linear programming is a mathematical modeling technique used to achieve the best outcome by maximizing or minimizing a linear function when subjected to several constraints. It is a simple technique in which we use linear functions to represent complex relationships and then discover the optimum points. It's used in many fields, such as business, engineering, economics, computer science, and operations research.

Linear programming is very beneficial for making business planning decisions, industrial engineering, and social & physical sciences.

On a personal and professional level, you are surrounded by the applications of Linear programming. When you're going from home to work and wish to take the shortest route, or when a project is due, you devise tactics to motivate your staff to work effectively, you apply linear programming.

Basic Terminologies Of Linear Programming Problems

Here is the list of basic terminologies of Linear programming problems-

Objective Function

It's a numerical value that should either be maximized or minimized. For instance, your primary goal is to increase profits while minimizing losses if you're in business.


The constraints are defined as the limitations of the decision variables. For example, if you are involved in some business, then the budget, number of workers, production capacity, space, etc. are the limitations or restrictions.

Non-negativity Restriction

The non-negativity limitation states that decision variables' values must be greater than or equal to 0.

Decision Variables

The variables that determine the output are known as decision variables. For instance, calculating the total area for growing wheat and barley is one of the decision variables for a farmer who wishes to plant wheat and barley.

Applications of Linear Programming Problems

Following is a list of areas where Linear programming is used.

Applications of Linear Programming

Human Resource Management

Linear programming helps the recruiting manager to handle difficulties relating to employees' selection, recruitment, training, and deployment to various departments within the company. The minimum number of personnel required in multiple shifts to meet the production schedule can be determined using linear programming.

Marketing Management

Marketers can use linear programming to examine the audience coverage of advertisements based on constraints like available media, advertising budget, and so on. A logistician can quickly determine the best distribution schedule for transporting a product from several warehouses to various market locations while keeping the total transportation cost minimum. Field agents can also use linear programming to find the quickest route to their destination.

Agriculture Management

Farmers can use linear programming to figure out which crops to cultivate and in what quantities to grow them in order to increase their profit.

Inventory Management

Linear programming is also useful for inventory management organizations in better managing raw materials and completed products. They can determine the best way to reduce inventory costs while keeping space and demand limits in mind.

Financial Management

Mutual fund businesses, financial firms, and banks use linear programming to choose investment portfolios of stocks, bonds, and other securities in order to optimize return on investment.

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  • Definition of Linear Programming
  • Mathematical Programming and Automation
  • Classification of Linear Programming Problems
  • Origins of Linear Programming
  • Economic Models and Linear Programming
  • Formulating Linear Programming Model
  • Industrial Applications of Linear Programming
  • Simplex Method
  • Linear Equation and Inequality Systems
  • Simplex Method Using Multipliers
  • Proof Of Simplex Algorithm & Duality Theorem
  • Finiteness Of Simplex Method Under Perturbation
  • Geometry Of Linear Programs
  • Variants Of Simplex Algorithm
  • Price Concept in Linear Programming
  • Pivoting, Vector Spaces, Matrices, and Inverses
  • Classic Transportation Problem
  • Games And Linear Programs
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