CBSE Class 12 Linear Programming (Applied Maths), Syllabus and Weightage

CBSE Class 12 Linear Programming: Linear Programming is a crucial part of CBSE Class 12 Applied Mathematics, but it can be tricky for students to grasp. This topic bridges math with real-world problem-solving, making it essential for acing board exams. Yet, mastering it requires more than just reading textbooks.

CBSE Class 12 Linear Programming

• 2x + 3y ≤ 12 (machine time constraint)
• 3x + y ≤ 9 (labor time constraint)
• x ≥ 0 and y ≥ 0 (products can't be negative)

CBSE Class 12 Linear Programming Practical Applications

1. Optimization: Linear programming aims to maximize/minimize an objective function within linear constraints. Think of it as finding the best solution for maximizing profit, minimizing cost, or achieving specific goals.
2. Mathematical Modeling: It involves creating mathematical models for real-world problems using linear relationships, usually expressed as equations or inequalities.
3. Linear Relationships: Linear programming deals with equations where variables are raised to the power of 1, and coefficients are constants. No squares, cubes, etc., making it simpler to work with.
4. Canonical Form: Problems are often expressed in canonical form, defining decision variables, formulating the objective function, and setting linear constraints.
5. Applications: Linear programming finds applications in planning, routing, scheduling, assignment, and design. For instance, it's used in logistics to optimize distribution routes and in finance for creating optimal investment portfolios.

CBSE Class 12 Linear Programming Syllabus

CBSE Class 12 Linear Programming Weightage

What to Expect From CBSE Class 12 Linear Programming?

• Using Math Language: You'll need to express problems using math terms and symbols, like forming objective functions and setting constraints. Being comfortable with math communication is crucial.
• Real-life Connections: Questions often relate linear programming to everyday situations, showing how these math techniques are useful beyond the classroom.
• Logical Thinking: Expect to demonstrate logical reasoning as you solve problems and find the best solutions. Critical thinking is key.
• Straightforward Calculations: Some questions require direct calculations, like finding optimal values or feasible regions.
• Complex Scenarios: Be ready for challenging questions with multiple variables, constraints, or additional factors that need careful consideration.
• Practice from Textbooks: Questions might resemble textbook exercises or examples, so practicing those types of problems is important.
• Algorithm Skills: You'll need to develop algorithms and logical approaches, understanding methods like the graphical and simplex methods.
• Related Concepts: Beyond linear programming, the exam might touch on topics like vectors, matrices, and coefficients if they're relevant to the problem.
• Real-world Applications: Questions may apply linear programming to various fields like planning, routing, or scheduling, requiring problem-solving skills in those contexts.

Components of CBSE Class 12 Linear Programming

Decision Variables:

Objective Function:

Constraints:

Non-Negative Restrictions:

CBSE Class 12 Linear Programming Study Material

NCERT Textbook:

Reference Books:

• "Introductory Methods of Numerical Analysis" by S.S. Sastry: This book explains Linear Programming in detail and in a way that's easy to grasp.
• "Linear Programming and Extensions" by George Dantzig: For those seeking a deeper understanding, this book offers advanced insights into the subject.

Sample Papers and Previous Year Question Papers: