Linear Programming

Board: CBSE Class: 12

Chapter Overview

Linear programming optimizes (maximizes/minimizes) a linear function Z = ax + by subject to constraints (linear inequalities). The feasible region contains all points satisfying constraints. The optimal solution lies at a corner point of the feasible region. The corner point method evaluates Z at each vertex. Unbounded regions may or may not have an optimal solution.

Topics Covered

Linear Programming Problem
Objective Function
Constraints
Feasible Region
Corner Point Method
Optimal Solution
Unbounded Solutions
Multiple Optimal Solutions

Key Formulas

Z = ax + by (objective)

Constraints: Ax + By <= C

Optimal value at a corner point

Real-World Applications

Applications: Manufacturing (resource allocation), transportation, logistics, portfolio optimization.

Study Tips

Tip: Graph constraints carefully

Tip: Identify the feasible region correctly

Tip: Always check all corner points