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1.Linear Programming – Introduction
Class 12 • Mathematics • NCERT
Linear Programming – Introduction
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This lesson introduces Linear Programming, its meaning, components, and terminology, as prescribed in the NCERT Class 12 syllabus.
Lesson Objectives
- Understand the concept of Linear Programming.
- Learn the components of an LPP.
- Identify objective functions and constraints.
- Prepare for NCERT board-level questions.
1. Meaning of Linear Programming
Linear Programming is a mathematical technique used to optimize (maximize or minimize) a linear objective function subject to a set of linear constraints.
Optimization means finding the best possible solution.
[ Image Placeholder: Real-life Optimization Example ]
2. Linear Programming Problem (LPP)
A problem that involves optimizing a linear objective function under linear constraints is called a Linear Programming Problem.
Both objective function and constraints must be linear.
[ Image Placeholder: General Structure of an LPP ]
3. Components of Linear Programming
Every Linear Programming Problem consists of the following components:
• Decision variables
• Objective function
• Constraints
• Non-negativity restrictions
• Objective function
• Constraints
• Non-negativity restrictions
[ Image Placeholder: Components of LPP ]
4. Objective Function
The objective function is a linear function that represents the quantity to be maximized or minimized.
Example: Maximize Z = ax + by
[ Image Placeholder: Objective Function Line ]
5. Constraints
Constraints are linear inequalities or equations that restrict the values of the decision variables.
Example: ax + by ≤ c
[ Image Placeholder: Graph of Constraints ]
6. Important NCERT Notes
• All relationships must be linear
• Variables must satisfy non-negativity conditions
• LPPs are solved graphically in Class 12
• High-weightage chapter for boards
• Variables must satisfy non-negativity conditions
• LPPs are solved graphically in Class 12
• High-weightage chapter for boards
Practice Questions (NCERT)
- Define Linear Programming.
- What is meant by optimization?
- What is an objective function?
- Define constraints.
- List components of an LPP.
- What are decision variables?
- Why non-negativity restrictions are required?
- Is quadratic function allowed in LPP?
- Is LPP part of NCERT Class 12 syllabus?
- Is LPP important for board exams?
✅ Show Answer Key
- Technique to optimize linear function
- Finding best possible solution
- Function to be maximized/minimized
- Restrictions on variables
- Variables, objective, constraints, non-negativity
- Variables representing decisions
- Variables cannot be negative
- No
- Yes
- Yes
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