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Chapters
2: Inverse Trigonometric Functions
3: Matrices
4: Determinants
5: Continuity and Differentiability
6: Application of Derivatives
7: Integrals
8: Application of Integrals
9: Differential Equations
10: Vector Algebra
11: Three Dimensional Geometry
▶ 12: Linear Programming
13: Probability
![NCERT solutions for Mathematics [English] Class 12 chapter 12 - Linear Programming - Shaalaa.com](/images/mathematics-english-class-12_6:f2fd4beccca84a5e862c6237e92b7e09.jpg "NCERT solutions for Mathematics [English] Class 12 chapter 12 - Linear Programming")
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Solutions for Chapter 12: Linear Programming
Below listed, you can find solutions for Chapter 12 of CBSE, Karnataka Board PUC NCERT for Mathematics [English] Class 12.
NCERT solutions for Mathematics [English] Class 12 12 Linear Programming EXERCISE 12.1 [Pages 403 - 404]
Solve the following Linear Programming Problems graphically:
Maximise Z = 3x + 4y
subject to the constraints : x + y ≤ 4, x ≥ 0, y ≥ 0.
Solve the following Linear Programming Problems graphically:
Minimise Z = – 3x + 4 y
subject to x + 2y ≤ 8, 3x + 2y ≤ 12, x ≥ 0, y ≥ 0.
Solve the following Linear Programming Problems graphically:
Maximise Z = 5x + 3y
subject to 3x + 5y ≤ 15, 5x + 2y ≤ 10, x ≥ 0, y ≥ 0
Solve the following Linear Programming Problems graphically:
Minimise Z = 3x + 5y
such that x + 3y ≥ 3, x + y ≥ 2, x, y ≥ 0.
Solve the following Linear Programming Problems graphically:
Maximise Z = 3x + 2y
subject to x + 2y ≤ 10, 3x + y ≤ 15, x, y ≥ 0.
Solve the following Linear Programming Problems graphically:
Minimise Z = x + 2y
subject to 2x + y ≥ 3, x + 2y ≥ 6, x, y ≥ 0.
Show that the minimum of Z occurs at more than two points.
Minimise and Maximise Z = 5x + 10 y
subject to x + 2y ≤ 120, x + y ≥ 60, x – 2y ≥ 0, x, y ≥ 0.
Show that the minimum of Z occurs at more than two points.
Minimise and Maximise Z = x + 2y
subject to x + 2y ≥ 100, 2x – y ≤ 0, 2x + y ≤ 200; x, y ≥ 0.
Show that the minimum of Z occurs at more than two points.
Maximise Z = – x + 2y, Subject to the constraints:
x ≥ 3, x + y ≥ 5, x + 2y ≥ 6, y ≥ 0.
Show that the minimum of Z occurs at more than two points.
Maximise Z = x + y, subject to x – y ≤ –1, –x + y ≤ 0, x, y ≥ 0.
Solutions for 12: Linear Programming
NCERT solutions for Mathematics [English] Class 12 chapter 12 - Linear Programming
Shaalaa.com has the CBSE, Karnataka Board PUC Mathematics Mathematics [English] Class 12 CBSE, Karnataka Board PUC solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. NCERT solutions for Mathematics Mathematics [English] Class 12 CBSE, Karnataka Board PUC 12 (Linear Programming) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.
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Concepts covered in Mathematics [English] Class 12 chapter 12 Linear Programming are Introduction of Linear Programming, Mathematical Formulation of Linear Programming Problem, Different Types of Linear Programming Problems, Graphical Method of Solving Linear Programming Problems, Linear Programming Problem and Its Mathematical Formulation, Introduction of Linear Programming, Mathematical Formulation of Linear Programming Problem, Different Types of Linear Programming Problems, Graphical Method of Solving Linear Programming Problems, Linear Programming Problem and Its Mathematical Formulation.
Using NCERT Mathematics [English] Class 12 solutions Linear Programming exercise by students is an easy way to prepare for the exams, as they involve solutions arranged chapter-wise and also page-wise. The questions involved in NCERT Solutions are essential questions that can be asked in the final exam. Maximum CBSE, Karnataka Board PUC Mathematics [English] Class 12 students prefer NCERT Textbook Solutions to score more in exams.
Get the free view of Chapter 12, Linear Programming Mathematics [English] Class 12 additional questions for Mathematics Mathematics [English] Class 12 CBSE, Karnataka Board PUC, and you can use Shaalaa.com to keep it handy for your exam preparation.
