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CBSE Class 12 Mathematics 2026 Main Paper 65/1/1 · Q303 Markslinear_programming

CBSE Class 12 Mathematics 2026 Main Paper 65/1/1 · Question 30 (Linear Programming)

Solve the following linear programming problem graphically: Minimize Z = 13x − 15y subject to constraints x + y ≤ 7, 2x − 3y + 6 ≥ 0, x ≥ 0, y ≥ 0.
Feasible polygon for x+y≤7 and 2x−3y+6≥0 in the first quadrant.
Feasible polygon for x+y≤7 and 2x−3y+6≥0 in the first quadrant.

✅ Step-by-Step Solution

Final Answer: Minimum Z = −30 at x=0, y=2.
  1. Plot constraints and find feasible region. Vertices: (0,0), (7,0), (3,4), (0,2).
  2. Evaluate Z: at (0,0)=0; (7,0)=91; (3,4)=39−60=−21; (0,2)=−30. Minimum is −30 at (0,2).
  3. Minimum Z = −30 at x=0, y=2.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Plot constraints and find feasible region. Vertices: (0,0), (7,0), (3,4), (0,2).
  • [2 marks] Evaluate Z: at (0,0)=0; (7,0)=91; (3,4)=39−60=−21; (0,2)=−30. Minimum is −30 at (0,2).
  • [0.5 marks] Minimum Z = −30 at x=0, y=2.

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All Questions in CBSE Class 12 Mathematics 2026 Main Paper 65/1/1

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