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CBSE Class 12 Mathematics 2026 Main Paper 65/4/1 · Q293 Markscorner_point_method

CBSE Class 12 Mathematics 2026 Main Paper 65/4/1 · Question 29 (Linear Programming)

Graphically maximize Z=200x+120y subject to x+y≤300, 3x+y≤600, x−y≥−100 and x,y≥0.
Feasible polygon at a common scale on both axes.
Feasible polygon at a common scale on both axes.

✅ Step-by-Step Solution

Final Answer: 48000 at (150,150).
  1. Draw the three boundary lines and shade the common feasible region in the first quadrant.
  2. The vertices (0,0),(200,0),(150,150),(100,200),(0,100) give objective values 0,40000,48000,44000,12000.
  3. The maximum is 48000 at (150,150).

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Draw the three boundary lines and shade the common feasible region in the first quadrant.
  • [2 marks] The vertices (0,0),(200,0),(150,150),(100,200),(0,100) give objective values 0,40000,48000,44000,12000.
  • [0.5 marks] The maximum is 48000 at (150,150).

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