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Step-by-step NCERT solutions for Linear Programming (Chapter 12, CBSE Class 12 Mathematics) — every question and answer worked out in full, not just the final result. You can also read the Linear Programming textbook chapter.

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What these solutions cover

All 10 questions in Linear Programming are solved in the PDF. Here's what's inside, exercise by exercise:

Exercise 12.1

  1. Solve the following Linear Programming Problem graphically: Maximise Z = 3x + 4y subject to the constraints: x + y ≤ 4, x ≥ 0, y ≥ 0.
  2. Solve the following Linear Programming Problem graphically: Minimise Z = –3x + 4y subject to x + 2y ≤ 8, 3x + 2y ≤ 12, x ≥ 0, y ≥ 0.
  3. Solve the following Linear Programming Problem graphically: Maximise Z = 5x + 3y subject to 3x + 5y ≤ 15, 5x + 2y ≤ 10, x ≥ 0, y ≥ 0.
  4. Solve the following Linear Programming Problem graphically: Minimise Z = 3x + 5y such that x + 3y ≥ 3, x + y ≥ 2, x, y ≥ 0.
  5. Solve the following Linear Programming Problem graphically: Maximise Z = 3x + 2y subject to x + 2y ≤ 10, 3x + y ≤ 15, x, y ≥ 0.
  6. Solve the following Linear Programming Problem 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.
  7. Solve the following Linear Programming Problem graphically: Minimise and Maximise Z = 5x + 10y subject to x + 2y ≤ 120, x + y ≥ 60, x – 2y ≥ 0, x, y ≥ 0.
  8. Solve the following Linear Programming Problem graphically: Minimise and Maximise Z = x + 2y subject to x + 2y ≥ 100, 2x – y ≤ 0, 2x + y ≤ 200; x, y ≥ 0.
  9. Solve the following Linear Programming Problem graphically: Maximise Z = –x + 2y, subject to the constraints: x ≥ 3, x + y ≥ 5, x + 2y ≥ 6, y ≥ 0.
  10. Solve the following Linear Programming Problem graphically: Maximise Z = x + y, subject to x – y ≤ –1, –x + y ≤ 0, x, y ≥ 0.
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More solutions in Mathematics Part II

07Integrals08Application of Integrals09Differential Equations10Vector Algebra11Three Dimensional Geometry13Probability
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More NCERT Solutions for Class 12

Read the Linear Programming textbook chapter / PDF, or browse all CBSE Class 12 Mathematics solutions.

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