Class 12 Mathematics Chapter 12 Linear Programming – Revision Notes

Linear Programming sets up a linear objective function subject to constraints, and this chapter explains the corner point method used to find where that function is maximised or minimised.

Last Updated: September 23, 2026

Key Concepts

• Objective function: Z=ax+by (maximize/minimize).
• Constraints: linear inequalities + non-negativity (x,y≥0).
• Feasible region: common region satisfying all constraints.

Corner Point Method

• Optimal Z occurs at a vertex of the feasible region.
• Evaluate Z at each corner point; pick max/min.
• Unbounded region: check if max actually exists.
• Equal Z at two adjacent corners ⇒ entire edge is optimal (multiple solutions).

One-Line Summary

Linear Programming optimizes a linear objective function over a feasible region defined by linear constraints, with the optimum always occurring at a corner point (vertex) of the region.

Quick visual: a worked diagram from the full Solutions page, for reference.

Frequently Asked Questions

What is the goal of a linear programming problem?
A linear programming problem aims to find the maximum or minimum value of a linear objective function, subject to a set of linear constraints, representing real-world limitations such as resources, cost, or time.

What is the significance of the feasible region and its corner points?
The feasible region is the set of all points satisfying every constraint simultaneously, and the Corner Point Theorem states that the optimal value of the objective function always occurs at one of the corner points of this region.

Written by Satish

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