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NCERT Maths Class 12 Chapter 12: Linear Programming

Linear Programming is an important chapter in Class 12 Mathematics that deals with finding the best possible solution to a problem under given conditions or constraints. It is widely used in business, economics, engineering, and management for decision-making and resource optimization.

What is Linear Programming?

Linear Programming is a mathematical technique used to maximize or minimize a linear objective function while satisfying a set of linear constraints. It helps in making efficient use of available resources.

Components of a Linear Programming Problem

Objective Function

The objective function represents the quantity that needs to be maximized or minimized, such as profit, production, or cost.

Chapter 12 - Linear Programming
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Constraints

Constraints are the conditions or limitations that must be satisfied while solving the problem. They are usually expressed as linear inequalities.

Feasible Region

The feasible region is the set of all possible solutions that satisfy the given constraints. The optimal solution is obtained from this region.

Graphical Method

In Class 12 Mathematics, linear programming problems are generally solved using the graphical method. This method helps visualize constraints and identify the optimal solution graphically.

Applications of Linear Programming

Linear programming is used in:

  • Business and finance
  • Production planning
  • Transportation and logistics
  • Resource allocation
  • Industrial management

It helps organizations improve efficiency and reduce costs.

Importance of the Chapter

Linear Programming connects mathematics with real-life decision-making problems. It is an important chapter for Class 12 Board Exams and helps students understand practical applications of mathematical optimization.

CBSE Exam Preparation Tips

Students should focus on objective functions, constraints, feasible regions, corner point methods, and graphical solutions. Regular practice of NCERT examples and application-based questions will help improve problem-solving skills and examination performance.

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