Mathbee CBSE Mathbee · CBSE Class 12 Maths
CBSE Class 12 Mathematics 2026 Supplementary Paper 65/7/2 · Q293 Markscorner_point_method

CBSE Class 12 Mathematics 2026 Supplementary Paper 65/7/2 · Question 29 (Linear Programming)

Minimize \(Z=4x+y\) subject to \(x+y\ge3\), \(x+2y\ge4\), \(x,y\ge0\), graphically.
Unbounded feasible region above x+y=3 and x+2y=4, clipped at x=6 and y=6 for display.
Unbounded feasible region above x+y=3 and x+2y=4, clipped at x=6 and y=6 for display.

✅ Step-by-Step Solution

Final Answer: Minimum 3 at (0,3).
  1. Intersect the boundary lines and retain the first-quadrant feasible sides above both lines.
  2. The vertices are (0,3),(2,1),(4,0), with Z=3,9,16. The unbounded boundary rays point along increasing positive coordinates and Z increases on both.
  3. Therefore the minimum is 3 at (0,3).

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Intersect the boundary lines and retain the first-quadrant feasible sides above both lines.
  • [2 marks] The vertices are (0,3),(2,1),(4,0), with Z=3,9,16. The unbounded boundary rays point along increasing positive coordinates and Z increases on both.
  • [0.5 marks] Therefore the minimum is 3 at (0,3).

Master Chapter 12: Linear Programming

Practise interactive questions, flashcards, visual mind maps, and timed board tests for Linear Programming.
📘 Chapter Notes & All Exercises 🚀 Open in Interactive Workspace →
← Previous Question
Find the sum of maximum and minimum values of sin x(1+cos x) on [0,π].
Next Question →
Find the line through (1,−1,2) parallel to the x-axis and its…

All Questions in CBSE Class 12 Mathematics 2026 Supplementary Paper 65/7/2

Q1Q2Q3Q4Q5Q6Q7Q8Q9Q10Q11Q12Q13Q14Q15Q16Q17Q18Q19Q20Q21Q22Q23Q24Q25Q26Q27Q28Q29Q30Q31Q32Q33Q34Q35Q36Q37Q38

Related Questions in Linear Programming

Class 12 Linear Programming · Mcq Single Correct
How many feasible solutions satisfy 3x+y≤12, x+2y≤10, x,y≥0?
Class 12 Linear Programming · Mcq Single Correct
The shaded first-quadrant region lies above both x+2y=4 and x+y=3. Which constraints describe…
Class 12 Linear Programming · Mcq Single Correct
Z=ax+by has maximum 42 at (4,6) and minimum 19 at (3,2). Find a,b.
Class 12 Linear Programming · Mcq Single Correct
A bounded feasible polygon has vertices (2,72),(15,20),(40,15). For Z=18x+9y, select the…
Class 12 Linear Programming · Mcq Single Correct
How many vertices does x−y≥0, 2y≤x+2, x,y≥0 have?
Class 12 Linear Programming · Mcq Single Correct
A bounded feasible polygon has vertices (0,3),(3,2),(0,5). Find the minimum of Z=11x+7y.