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