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Chapter 12 Class 12 Linear Programming

Master Chapter 12 Class 12 Linear Programming with comprehensive NCERT Solutions, Practice Questions, MCQs, Sample Papers, Case Based Questions, and Video lessons.

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Updated according to new NCERT - 2026-25 NCERT Books.

Learn Chapter 12 Linear Programming of Class 12, free with solutions of all NCERT Questions, Examples. Ideal for your CBSE Board Exams.

 

In Chapter 6 Class 11, Linear Inequalities, we learned how to make a graph of equations with Inequalities.

In this chapter, we will use the same methods, and also learn how to form equations and then solve.

 

Here, we will try to find the minimum or maximum value of an equation within a given set of conditions.

For example: Maximise profit, if Number of hours worked < 10, etc.

These type of problems, where we need to find minimum or maximum values, based on some conditions are known as Optimization Problems. A sub-part of these optimization problems are Linear Programming Problems... 

which we will study in this chapter.

 

The topics in this chapter include:

  • Finding minimum or maximum value of Z (known as objective function), using constraints - We use corner point method, and the basics which we learned in Linear Equality Chapter of Class 11. 
  • Handing cases where region is not feasible or unbounded.
  • In the previous topic, the equation is already given to us. But, we also need to create the equations, and then solve. We cover different types of problems like Diet, Manufacturing, Transport and Other Problems. In these questions, we first make the equations, and then find minimum or maximum value of Z.

 

Serial order wise

Ex 12.1 Start Learning
Examples Start Learning
Case Based Questions (MCQ) Start Learning
NCERT Exemplar - MCQs Start Learning
Forming equations and solving Start Learning
Questions - Forming equations and solving Start Learning

Concept wise

Linear equations given - Bounded Start Learning
Linear equations given - Not feasible Start Learning
Linear equations given - Unbounded Start Learning
Diet problems Start Learning
Manufacturing problems Start Learning
Other questions Start Learning
Transport problems Start Learning

Why Learn This With Teachoo?

Updated according to new NCERT - 2026-25 NCERT Books.

Learn Chapter 12 Linear Programming of Class 12, free with solutions of all NCERT Questions, Examples. Ideal for your CBSE Board Exams.

 

In Chapter 6 Class 11, Linear Inequalities, we learned how to make a graph of equations with Inequalities.

In this chapter, we will use the same methods, and also learn how to form equations and then solve.

 

Here, we will try to find the minimum or maximum value of an equation within a given set of conditions.

For example: Maximise profit, if Number of hours worked < 10, etc.

These type of problems, where we need to find minimum or maximum values, based on some conditions are known as Optimization Problems. A sub-part of these optimization problems are Linear Programming Problems... 

which we will study in this chapter.

 

The topics in this chapter include:

  • Finding minimum or maximum value of Z (known as objective function), using constraints - We use corner point method, and the basics which we learned in Linear Equality Chapter of Class 11. 
  • Handing cases where region is not feasible or unbounded.
  • In the previous topic, the equation is already given to us. But, we also need to create the equations, and then solve. We cover different types of problems like Diet, Manufacturing, Transport and Other Problems. In these questions, we first make the equations, and then find minimum or maximum value of Z.