# Linear Programming Notes, Class 12 Mathematics | SwaVid

Linear Programming, NCERT Class 12 Mathematics: notes with key ideas, formulas, common mistakes and 3 quick checks with worked answers.

Canonical: https://www.swavid.com/cbse/class-12/maths/chapter/linear-programming

Source: https://www.swavid.com/cbse/class-12/maths/chapter/linear-programming

# Linear Programming

## Formulas and definitions

## Key ideas

## Common mistakes

## Quick checks

## Keep going

## Questions parents ask

## Class 12 Mathematics on SwaVid

### Linear programming problem

### Feasible region and solutions

### Corner point theorem

### Corner point method

### Unbounded feasible region

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SwaVid › CBSE › Class 12 › Mathematics › Linear Programming

Notes written by SwaVid from the NCERT textbook.

Class 12 Mathematics, Chapter 12. Key ideas, formulas and common mistakes.

CBSE does not print marks for a single chapter.

Short answer. This chapter deals with linear programming problems, which aim to optimise a linear objective function subject to a set of linear inequalities called constraints. Students learn to determine the feasible region graphically and find optimal solutions using the corner point method.

Source: NCERT Mathematics Part II (Reprint 2026-27) , Chapter 12, Linear Programming

A linear programming problem (LPP) seeks to maximise or minimise a linear objective function Z = ax + by, subject to linear constraints and non-negative restrictions on decision variables x and y.

The common region determined by all the given constraints, including the non-negative restrictions x ≥ 0 and y ≥ 0, is called the feasible region. Any point inside or on the boundary of this region represents a feasible solution to the problem.

Theorem 1 states that when an objective function Z has an optimal value, it occurs at a corner point (vertex) of the feasible region. Theorem 2 states that if the feasible region is bounded, Z attains both a maximum and a minimum value at the corner points.

Find the feasible region and determine its corner points either by inspection or by solving the boundary equations. Evaluate Z at each corner point; the largest and smallest values are the maximum and minimum values respectively when the region is bounded.

If the feasible region is unbounded, M is the maximum value of Z only if the open half-plane ax + by > M has no point in common with the feasible region. Similarly, m is the minimum value only if ax + by M shares no common points with the feasible region before concluding M is the maximum.

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