NCERT Solutions for Class 12 Mathematics Chapter 12 Linear Programming

This worksheet provides complete and accurate NCERT Solutions for Class 12 Mathematics Chapter 12 Linear Programming. This chapter introduces students to the concept of optimisation using linear inequalities and helps them understand how to find maximum or minimum values of a function. It is an important chapter as it builds problem-solving and analytical skills required in higher mathematics and real-life applications. The worksheet strictly follows NCERT guidelines and ensures that all answers are correct and aligned with the textbook.

Chapter summary: stories, poems & themes

This chapter is concept-based and does not include stories or poems. It focuses on mathematical problem-solving using graphical methods. Students learn how to form linear programming problems, identify constraints, and determine feasible regions. The main theme of the chapter is optimisation, where students find the best possible solution under given conditions. The chapter is activity-based in terms of graph drawing and interpretation.

What this NCERT chapter covers?

• Understanding linear programming problems and objective functions 
• Formation of linear inequalities and constraints 
• Graphical representation of inequalities 
• Identification of feasible region and corner points 
• Application of corner point method to find optimal solutions 
• Interpretation of maximum and minimum values in real-life contexts 

How to use these NCERT solutions?

Students should first attempt all questions from the worksheet on their own. After solving, they can refer to these NCERT Solutions to verify their answers and understand the correct method. Parents and teachers can use this worksheet to guide students step-by-step. All solutions follow the exact NCERT order and structure, making revision easy and systematic. This helps students build confidence and improve accuracy.

Student tips & learning tricks

Students should carefully draw graphs with proper scales to avoid mistakes in identifying feasible regions. Always check all constraints before selecting the final region. Evaluate the objective function at all corner points to ensure the correct maximum or minimum value. Avoid skipping steps while solving equations, as accuracy is important in linear programming problems.

Why NCERT solutions are important?

NCERT Solutions help students understand concepts clearly and follow the correct method as prescribed by CBSE. They build a strong foundation for exams and competitive studies. These solutions ensure that students learn accurate problem-solving techniques and gain confidence in answering similar questions in assessments.

Complete answer key – NCERT solutions

Exercise 12.1

1. 
Maximum Z = 16 at (0, 4)

2. 
Minimum Z = –12 at (4, 0)

3. 
Maximum Z = 235/19 at (20/19, 45/19)

4. 
Minimum Z = 7 at (3/2, 1/2)

5. 
Maximum Z = 18 at (4, 3)

6. 
Minimum Z = 6 at (0, 3) and (6, 0)

7. 
Minimum Z = 300 at (60, 0) 
Maximum Z = 600 at (120, 0) and (60, 30)

8. 
Minimum Z = 100 at (0, 50) and (20, 40) 
Maximum Z = 400 at (0, 200)

9. 
Maximum Z = 1 at (3, 2)

10. 
No feasible solution

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