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CBSE Class 12 Mathematics 2026 Supplementary Paper 65/7/1 · Q242 Marksfeasible_regions

CBSE Class 12 Mathematics 2026 Supplementary Paper 65/7/1 · Question 24 (Linear Programming)

Shade the feasible region for \(2x+y\le70\), \(x+y\le40\), \(x,y\ge0\), and list its vertices.
Shaded feasible polygon for 2x+y≤70, x+y≤40, x,y≥0.
Shaded feasible polygon for 2x+y≤70, x+y≤40, x,y≥0.

✅ Step-by-Step Solution

Final Answer: (0,0),(35,0),(30,10),(0,40).
  1. Draw the two boundary lines and use the first-quadrant sides containing the origin.
  2. The axis bounds are x≤35 and y≤40. Solving both boundary equalities gives x=30,y=10.
  3. The feasible polygon has vertices (0,0),(35,0),(30,10),(0,40).

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Draw the two boundary lines and use the first-quadrant sides containing the origin.
  • [1 mark] The axis bounds are x≤35 and y≤40. Solving both boundary equalities gives x=30,y=10.
  • [0.5 marks] The feasible polygon has vertices (0,0),(35,0),(30,10),(0,40).

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