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A linear programming… (Class 12 Maths SQP 2024-25, Q16)

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MathsCBSE Class 12 · Sample paper, session 2024-25 · 1 mark · MCQ

CBSE Class 12 Mathematics sample paper 2024-25: question 16

From the official CBSE sample question paper for 2024-25, section A, question 16, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q16 · 1 mark · MCQLinear Programming

A linear programming problem (LPP) along with the graph of its constraints is shown below. The corresponding objective function is: , which has to be minimized. The smallest value of the objective function Z is 134 and is obtained at the corner point .

(Note: The figure is not to scale.)

The optimal solution of the above linear programming problem __________.

  1. (A)does not exist as the feasible region is unbounded.
  2. (B)does not exist as the inequality does not have any point in common with the feasible region.
  3. (C)exists as the inequality has infinitely many points in common with the feasible region.
  4. (D)exists as the inequality does not have any point in common with the feasible region.

Figure in the paper: Unbounded shaded feasible region with corner point P(3,8). Lines: 4x+y=20 (intercepts A1(5,0), B1(0,20)), 2x+3y=30 (intercepts A2(15,0), (0,10)), and dotted line 18x+10y=134 passing through P(3,8) and meeting y-axis at B2(0,10). See it in the official paper.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2024-25.

Hints

Open one hint at a time and try again before the next.

Hint 1

Unbounded region does not automatically mean no minimum.

Hint 2

Check the open half-plane .

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

  1. For an unbounded region, the corner value 134 is the minimum if the half-plane has no point in common with the feasible region.

  2. That is the case here, so the optimal solution exists: min at . Option (D).

    1 mark

Answer: Option (D)

Where the marks are

  • Applies the unbounded-region test (1 mark)

Revise the chapter

Practise this chapterBoard-style questions from Linear Programming, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2024-25: every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.