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# Chapter 12 Class 12 Linear Programming

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Updated according to new NCERT - 2024-25 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.

## Concept wise

What's in it?

Updated according to new NCERT - 2024-25 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.