Skip to content

In the Linear Programming… (Class 12 Maths 2025, Q30)

questionbuddy.in/q/cbse-12-maths-2025-65-7-1-q30-linear-programming-problem-objective-function

MathsCBSE Class 12 · Board exam 2025, set 65/7/1 · 3 marks · Short answer

CBSE Class 12 Mathematics 2025: question 30

Set in the CBSE Class 12 board exam of 2025, paper 65/7/1, 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

In the Linear Programming Problem for objective function subject to constraints

find the minimum value of Z.

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

For '≥' constraints, the feasible region lies on the side of each line away from the origin and is unbounded.

Hint 2

Find the intersection of the two lines, evaluate Z at every corner, and remember the extra check needed for an unbounded 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.

  1. Graph: passes through and , and passes through and . Both inequalities are '≥', so the region lies away from the origin. With the feasible region is unbounded, lying above both lines in the first quadrant. Solving the two lines: gives , so and . The corner points are , and .

    1½ marks
  2. Corner point
    A(0, 20)200
    B(3, 8)134
    C(15, 0)270
    1 mark

  3. The region is unbounded, so draw the half-plane . It has no point in common with the feasible region. Hence the minimum value of Z is 134 at (3, 8).

    ½ mark

Answer: Minimum Z = 134 at (3, 8)

Where the marks are

  • Correct graph of the unbounded feasible region with corner points (1½ marks)
  • Evaluates Z at A, B, C correctly (1 mark)
  • Checks the half-plane and concludes min Z = 134 at (3,8) (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 paper2025 board paper, set 65/7/1: 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.