# MTH601-Linear Programming Introduction and Concepts | Operations Research Lecture No 3

Mth601 Short Lectures | Linear Programming Introduction in urdu and hindi is very important in Concepts Operations Research in this Lecture No 3 #LinearProgramming #OperationsResearch #LP. In this online video lecture of linear programming concept and its introduction is explained in Urdu and Hindi. Linear programming is the basic and fundamental numerical skill in Operation Research to solve 2 dimensional real life wordy problems.

## What is Linear programming?

The world linear stand for indicating the relationships between different variables of degree one whereas another word programming means planning and refers to the process of selecting best course of action from various alternatives. Thus, linear programming is a mathematical technique for allocating limited resources is optimum manner.

In the words of William M. Fox, “Linear programming is a planning technique that permits some objective function to be minimized or maximized within the framework of given situational restrictions.” • Linear Programming (LP) is a mathematical modelling technique useful for allocation of limited resources such as material, machines etc to several competing activities such as projects, services etc.

§Linear programming is a mathematical technique designed to aid managers in allocating resources (such as labor, capital, or energy. Machines) among competing activities. §It reflects, in the form of a model, the organization’s attempt to achieve some objective (frequently, maximizing profit contribution, maximizing rate of return, minimizing costs) §In view of limited or constrained resources (available capital or labor, service levels, available machine time, budgets).

#### Definition

The linear programming technique can be said to have a linear objective function that is to be optimized (either maximized or minimized) subject to linear equality or inequality constraints and sign restrictions on the variables.

#### What is Linear Relation

§A linear relationship (or linear association) is a statistical term used to describe a straight-line relationship between a variable and a constant. Linear relationships can be expressed either in a graphical format or as a mathematical function (equation).

#### Linear Objective Function

The linear function is called the objective function , of the form f(x,y)=ax+by+c. The solution set of the system of inequalities is the set of possible or feasible solution , which are of the form (x,y) .

#### History of LPP

§The problem of solving a system of linear inequalities dates back at least as far as Fourier, who in 1827 published a method for solving them, and after whom the method of Fourier–Motzkin elimination is named. §In 1939 a linear programming formulation of a problem that is equivalent to the general linear programming problem was given by the Soviet economist Leonid Kantorovich, who also proposed a method for solving it.

### Applications/Uses of LP

§A company produces agricultural fertilizers. It is interested in minimizing costs while meeting certain specified levels of nitrogen, phosphate, and potash by blending together a number of raw materials. §An investor wants to maximize his or her rate of return by investing in stocks and bonds. The investor can set specific conditions that have to be met including availability of capital. §A company wants the best possible advertising exposure among a number of national magazines, and radio and television commercials within its available capital requirements.

§An oil refinery blends several raw gasoline and additives to meet a car manufacturer’s specifications while still maximizing its profits. §A city wants to maximize the daytime use of recreational properties being proposed for purchase with a limited capital available.

#### Solution of Linear Programming

• Graphical method
• Simplex method
• Duality Method
• Big M method §Game theory

### Standard form of LPP

What is Linear programing , its History and Applications will be detailed in this lecture in #Hindi and #URDU Operations Research Introduction and OR Process for BSIT, BSCS BBA and BSSE classes . These video series of Operations Research lectures in Hindi and URDU are recorded to help students. These are short videos Lectures giving more details. #VU #VirtualUniversity #GCUF

## Lecture Topics for Today

• 1:00 Introduction of Linear programming
• 10:14 Definition of Linear Programming
• 11:42 Linear Relation and Linear Objective Function
• 15:54 history of Linear Programming
• 18:52 Uses, Examples and Application of Linear Programming
• 23:12 Linear Programming Methods

### Linear Programming Introduction and Concepts | Operations Research Lecture No 3

#### Author: Habibullah Qamar

Its me Habib Ullah Qamar working as a Lecturer (Computer Sciences) in Pakistan. I have an MS(M.Phil) degree in computer sciences with specialization in software engineering from Virtual University of Pakistan Lahore. I have an experience of more than 15 years in the filed of Computer Science as a teacher. Blog Writing is my passion. I have many blogs, This one is special made with the aim of providing 100% Free online coaching and training to the students of under-graduate and postgraduate classes. Most of the students enrolled in computer sciences, information technology, software engineering and related disciplines find it difficult to understand core concepts of programming and office automation. They find difficult in understanding and solving their assignments.