In a Linear Programming Problem, the objective function Z = 5x + 4y needs to be maximised under constraints 3x + y ≤ 6, x ≤ 1, x, y ≥ 0. Express the LPP on the graph and shade the feasible region and mark the corner points.

MathsCBSE Class 12 · Board exam 2025, set 65/7/1 · 2 marks · Very short answer

CBSE Class 12 Mathematics 2025: question 24

Set in the CBSE Class 12 board exam of 2025, paper 65/7/1, section B, question 24, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q24 · 2 marks · Very short answerLinear Programming

In a Linear Programming Problem, the objective function $Z = 5 x + 4 y$ needs to be maximised under constraints $3 x + y \leq 6$ , $x \leq 1$ , $x, y \geq 0$ . Express the LPP on the graph and shade the feasible region and mark the corner points.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 65/7/1.

Hints

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

Hint 1

Draw $3 x + y = 6$ using its intercepts and draw the vertical line $x = 1$ .

Hint 2

Use the test point (0,0) to choose the side of each line, then find where $x = 1$ meets $3 x + y = 6$ .

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.

Plot the boundary lines: $3 x + y = 6$ passes through $(2, 0)$ and $(0, 6)$ , and $x = 1$ is a vertical line through $(1, 0)$ . Test with the origin: $0 \leq 6$ and $0 \leq 1$ are both true, so the region lies on the origin side of both lines. With $x, y \geq 0$ the region is in the first quadrant.
1½ marks
Feasible region and corner points: The lines $x = 1$ and $3 x + y = 6$ meet at $(1, 3)$ . The shaded feasible region is the bounded quadrilateral $O C B A$ , between the y-axis and $x = 1$ , above the x-axis and below $3 x + y = 6$ . Its corner points are $O (0, 0)$ , $C (1, 0)$ , $B (1, 3)$ and $A (0, 6)$ .
½ mark

Answer: Feasible region OCBA with corner points O(0,0), C(1,0), B(1,3), A(0,6).

Where the marks are

Correct plotting of the lines $3 x + y = 6$ and $x = 1$ (1½ marks)
Correct shading of the feasible region and marking of the corner points (½ mark)

Revise the chapter

Chapter: Linear Programming (notes, formulas, where marks are lost and every past question)
Topic: Feasible Region and Constraints

Practise this chapterBoard-style questions from Linear Programming, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 65/7/1: every question, by section.

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CBSE Class 12 Mathematics 2025: question 24

Hints

Step-by-step solution

Revise the chapter

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