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CBSE Class 12 Mathematics 2026 Main Paper 65/2/3 · Q313 Markscorner_point_method

CBSE Class 12 Mathematics 2026 Main Paper 65/2/3 · Question 31 (Linear Programming)

Graphically maximize Z=4500x+5000y subject to x+y≤250, 25x+40y≤7000 and x,y≥0.
Feasible polygon with vertices (0,0), (250,0), (200,50), and (0,175), at the same scale on both axes.
Feasible polygon with vertices (0,0), (250,0), (200,50), and (0,175), at the same scale on both axes.

✅ Step-by-Step Solution

Final Answer: 1150000 at (200,50).
  1. Plot the two boundary lines and shade their common lower side in the first quadrant. Their intersection is (200,50).
  2. The vertices (0,0),(250,0),(200,50),(0,175) give objective values 0,1125000,1150000,875000.
  3. The maximum is 1150000 at (200,50).

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Plot the two boundary lines and shade their common lower side in the first quadrant. Their intersection is (200,50).
  • [2 marks] The vertices (0,0),(250,0),(200,50),(0,175) give objective values 0,1125000,1150000,875000.
  • [0.5 marks] The maximum is 1150000 at (200,50).

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