MathsCBSE Class 12 · Board exam 2026, set 65/1/1 · 3 marks · Short answer

CBSE Class 12 Mathematics 2026: question 30

Set in the CBSE Class 12 board exam of 2026, paper 65/1/1, section C, question 30, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q30 · 3 marks · Short answerLinear Programming

Solve the following linear programming problem graphically :
Minimize $Z = 13 x - 15 y$
Subject to constraints
$x + y \leq 7$ ,
$2 x - 3 y + 6 \geq 0$ ,
$x \geq 0, y \geq 0$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 65/1/1.

Hints

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

Hint 1

Plot each boundary line using its intercepts and test the origin to decide the side to shade.

Hint 2

Find the intersection of $x + y = 7$ and $2 x - 3 y = - 6$ to get a corner.

Hint 3

Evaluate Z at each corner of the bounded region.

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.

Draw the lines $x + y = 7$ (through $(7, 0)$ , $(0, 7)$ ) and $2 x - 3 y + 6 = 0$ (through $(- 3, 0)$ , $(0, 2)$ ) in the first quadrant. $(0, 0)$ satisfies both inequalities, so shade the side containing the origin. They intersect where $x = 7 - y$ , $2 (7 - y) - 3 y = - 6 \Rightarrow y = 4, x = 3$ . The bounded feasible region is the quadrilateral with corners $O (0, 0)$ , $(7, 0)$ , $(3, 4)$ , $(0, 2)$ .
1½ marks
Corner point $Z = 13 x - 15 y$
(0, 0) 0
(7, 0) 91
(3, 4) 39 − 60 = −21
(0, 2) −30
1 mark
Minimum value of $Z$ is $- 30$ at $x = 0, y = 2$ .
½ mark

Corner point	$Z = 13 x - 15 y$
(0, 0)	0
(7, 0)	91
(3, 4)	39 − 60 = −21
(0, 2)	−30

Answer: Minimum Z = −30 at (0, 2)

Where the marks are

Correct graph and shading of bounded feasible region with corners (0,0), (7,0), (3,4), (0,2) (1½ marks)
Evaluates Z at all corner points (1 mark)
States minimum −30 at (0, 2) (½ mark)

Revise the chapter

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

Practise this chapterBoard-style questions from Linear Programming, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 65/1/1: 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.

CBSE Class 12 Mathematics 2026: question 30

Hints

Step-by-step solution

Revise the chapter

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