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CBSE Class 12 Mathematics 2026 Supplementary Paper 65/7/3 · Q303 Markscorner_point_method

CBSE Class 12 Mathematics 2026 Supplementary Paper 65/7/3 · Question 30 (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).

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All Questions in CBSE Class 12 Mathematics 2026 Supplementary Paper 65/7/3

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