Class 12th Math Liner Programming NCERT Solution CBSE 2023
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NCERT Solutions for Class 12 Maths Chapter 12

Chapter 12 Linear Programming

Chapter 12 of CBSE Grade 12 Math covers important concepts of linear programming. Students must have a good understanding of linear programming concepts in order to score well in exams. Being thorough with the questions in the text is one of the first steps. So Vidyakul has provided the Grade 12 Math NCERT notes for Chapter 12 for free to help them prepare better.


Points to Remember

Below we have provided the crucial points that students must remember about the chapter to score well and achieve great results:

  • Linear programming Class 12 Math concepts assist in determining the maximisation or minimisation of various quantities from a general class of problems.

  • This is known as an optimisation problem. The linear programming for Class 12 concepts include determining a maximum profit, minimum cost, or minimum use of resources, among other things.

  • A linear objective function is a linear function of the form Z = ax + by, where a and b are constants, that must be minimised or maximised.

  • An optimisation problem is one in which the goal is to maximise or minimise a linear function (say, of two variables x and y) under certain constraints defined by a set of linear inequalities.

  • The feasible region (or solution region) for a linear programming problem is the common region determined by all the given constraints, including non-negative constraints (x ≥ 0, y ≥ 0). An infeasible region is any region that is not feasible.

  • These points within and on the boundary of the feasible region represent feasible constraints solutions. An infeasible solution is defined as any point outside the feasible region.

  • An optimal solution is any point in the feasible region that gives the optimal value (maximum or minimum) of the objective function.

Topics and Sub- topics 

In earlier grades, students might have studied systems of linear equations and their applications. Hence, it is expected that students will be able to do sums from linear equations independently. Moreover, the 12th CBSE Maths book and the in-text exercises are very important for the students who want to appear for the board exams and competitive exams in the future.

To help students with their exam preparations, Vidyakul provides fun learning videos on its platform that engage students with their studies. The topics and sub-topics included in the Linear Programming chapter are as follows:

Sr. No



Linear Programming Problem and its Mathematical Formulation


Different Types of Linear Programming Problems


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