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RD Sharma Class 12 Maths Solutions Chapter 30 - Linear programming

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RD Sharma Solutions for Class 12 Maths Chapter 30 - Linear programming - Free PDF Download

RD Sharma Class 12 Linear Programming  Solutions are given here. In this Chapter, we are going to discuss the concepts of Linear Programming . It is defined as the process of taking various linear inequalities related to some situation and trying to find the best obtainable value under those conditions. Linear Programming  is widely used in Mathematics and also it is used in other fields such as economics, business, telecommunication, and manufacturing fields.

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Class 12 RD Sharma Textbook Solutions Chapter 30 - Linear programming

Introduction to RD Sharma Class 12 Linear Programming Solutions

Linear programming is a method of optimising problems with some constraints. The main objective of linear programming is to maximize or minimize the numerical value of the function. It consists of linear functions which are subjected to the constraints in the form of linear equations or in the form of linear inequalities. It is considered an important technique which is used to find the optimum resource utilisation. 

We have provided step by step solutions for all exercise questions given in the pdf of Class 12 RD Sharma Chapter 30 - Linear programming. All the Exercise questions with solutions in Chapter 30 - Linear programming are given below:

 

The Topics Covered in Linear Programming Are as Follows

  • A mathematical formulation of L.P.

  • Introduction, related terminology such as objective function, constraints.

  • Different types of linear programming (L.P.) problems.

  • Problems and their graphical method of solution in two variables.

  • Feasible and infeasible solutions.

  • Optimal feasible solutions for the problems (up to three non-trivial constraints).

  • Feasible and infeasible regions (bounded and unbounded)

 

Characteristics of Linear Programming

The following are the five characteristics of linear programming:

Constraints – The constraints are the restrictions or limitations on the decision variables in the function. It usually limit the value of the decision variables

Objective Function – The objective function of a problem should be specified in a quantitative way.

Linearity – The relation between two or more variables in the function must be linear. 

Finiteness –  There should be a finite and infinite number of  input and output numbers. In case, if the function has infinite factors then the optimal solution is not feasible. 

Non-Negativity – It cannot be a negative value. The variable value can be positive or zero.

 

Following Are Steps of Defining a Linear Programming Problem Generically

  • Identify the decision variables

  • Write the objective function

  • Mention the constraints

  • Explicitly state the non-negativity restriction

 

RD Sharma Solutions for Class 12 – Chapter 30 – Key Concepts

For the advantage of students, the RD Sharma Solutions for Class 12 Math Chapter 30 Linear Programming  are provided here. Students preparing for CBSE, ICSE, or other state board exams prefer the RD Sharma Books for exams and other test preparation, such as admission exams for various jobs and degrees. The Maths specialists at Vedantu have created RD Sharma Solutions for Class 12 specifically for you.

RD Sharma Solutions generally cover the topics that are most likely to be tested and provide high-quality content on practically all Mathematics disciplines, including algebra, geometry, statistics, and more. We provide RD Sharma Solutions for CBSE Class 6th, 7th, 8th, 9th, 10th, 11th, and 12th students at Vedantu.

The fundamentals of Linear Programming  will be discussed in this section. Linear Programming  is the process of taking a set of linear inequalities and determining the "optimal" result that can be obtained under those constraints. The following are some examples of Linear Programming  topics:

  • The Mathematical formulation of L.P.\sIntroduction, related terminology such as objective function, constraints.

  • Different types of Linear Programming  (L.P.) problems.

  • Problems, graphical solution approach for two-variable problems.

  • Feasible and infeasible solutions.

  • Optimal feasible solutions (up to three non-trivial constraints).

  • Feasible and infeasible regions (bounded and unbounded).

 

Conclusion

In order to help students understand the concept clearly we are offering RD Sharma solutions .Pdf consist of conceptual problems along with solved examples including step by step method. RD Sharma Class 12 Maths Chapter 30 Solutions will help students to develop better maths solving skills and prepare efficiently for the exams. Our Subject matter experts have prepared the solutions and even designed the different solving approaches to problems so that students will be having a lot of fun while solving it.

FAQs on RD Sharma Class 12 Maths Solutions Chapter 30 - Linear programming

1. What is Linear Programming ?

Linear Programming  is a technique for solving problems that are constrained. The basic goal of Linear Programming  is to maximize or minimize the function's numerical value. It is made up of linear functions that are constrained by constraints in the form of linear equations or linear inequalities. It is regarded as a crucial strategy for determining the best resource utilization.

2. What are the topics covered in Linear Programming ?

A Mathematical formulation of L.P.

A Mathematical formulation of L.P.  Introduction, related terminology such as objective function, constraints.

  • Feasible and infeasible regions (bounded and unbounded)

  • Different types of Linear Programming  (L.P.) problems.

  • Problems and their graphical method of solution in two variables.

  • Feasible and infeasible solutions.

  • Optimal feasible solutions for the problems (up to three non-trivial constraints)

3. What are the characteristics of Linear Programming ?

The five properties of Linear Programming  are as follows:

  • Constraints - Constraints are restrictions or limitations on the function's decision variables. It usually sets a limit on how much the decision variables can be worth.

  • Problem's Objective Function - The problem's objective function should be quantified.

  • Linearity - The function's relationship between two or more variables must be linear.

  • Finiteness - The number of input and output numbers should be finite and infinite, respectively. If the function contains infinite factors, the optimal solution is impossible to achieve.

  • Non-Negativity — The value cannot be negative. The value of the variable can be either positive or negative.

4. What are the steps defining Linear Programming ?

The Steps to Defining a Linear Programming  Problem, in General, are Listed Below.

  • Determine the variables that affect your decision.

  • Create the goal function.

  • Mention the limitations.

  • Clearly state the non-negativity constraint.

5. What are some examples of Linear Programming  applications?

The following are some examples of Linear Programming  applications in various domains.

  • Engineering - It is utilized to create and solve production challenges since it aids in shape optimization.

  • Companies employ linear expressions to maximize profit in efficient manufacturing.

  • Energy Industry - It gives ways for optimizing the industry's electric power system.

  • Transportation Optimisation - This is done to save money and time.

6. What are the benefits of using Vedantu's RD Sharma solution?

Vedantu's RD Sharma solutions include both basic and advanced level questions, as well as their answers. Solutions are available in a variety of techniques and are simple to comprehend. The website's correct solutions are written in a student-friendly way, making learning easier. The solutions are created by industry specialists to assist students in achieving good results on their board exams. VEDANTU'S teachers have produced Chapter-by-Chapter solutions to assist students in this endeavor.

7. What distinguishes the many types of Linear Programming ?

The various types of Linear Programming  are as follows:

  • To address Linear Programming  issues, the Simplex technique is utilized.

  • R is a computer language that is used to address Linear Programming  problems.

  • Solving Linear Programming  problems with a graphical way

8. Why students should refer to the RD Sharma solution given by Vedantu?

RD Sharma solutions provided by Vedantu contains basic as well as an advanced level of questions and their solutions. Solutions are available with different solving approaches and are easy to understand.