Introduction to NCERT Exemplar Solutions for Class 12 Maths Chapter 12 – Linear Programming
The chapter on Linear Programming introduces students to a very practical area of class 12 mathematics that deals with optimization. The NCERT Exemplar Maths Solutions guide learners in understanding how to formulate and solve real-world problems where resources are limited and must be used efficiently. The chapter begins with the basics of linear inequalities in two variables. The solutions explain how to represent these inequalities graphically and identify feasible regions that satisfy given conditions. Step-by-step examples ensure that students can visualize the problem clearly before solving it. The concept of an objective function is introduced, which represents the quantity to be maximized or minimized. The Exemplar Solutions illustrate how to test values of the objective function at corner points of the feasible region to obtain the required optimum value. This is known as the corner point method and is a key technique in linear programming.
The exercises include problems from business, economics, and daily life situations, such as minimizing cost, maximizing profit, or optimizing transportation. These examples show the practical relevance of linear programming, making mathematics more engaging and useful for learners. The Exemplar provides a variety of problems ranging from straightforward to complex, which strengthens logical thinking and problem-solving ability. Graphical representation is emphasized throughout, ensuring that students develop both visual and analytical skills. Since linear programming is an important topic in board examinations and also has applications in management, operations research, and logistics, mastering it is essential. The NCERT Exemplar Solutions make this possible by presenting clear explanations, systematic methods, and well-structured exercises. Thus, this chapter equips students with powerful mathematical tools to make decisions in real-life scenarios. By practicing regularly from the Exemplar, learners gain accuracy, speed, and confidence in solving optimization problems.