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Class 12 Linear Programming · Long Answer3 Marksgraphical_optimization

Class 12 Maths · Linear Programming · Long Answer #35

Maximize Z=5*x + 8*y subject to x + y ≤ 5; -x - y ≤ -5; x ≤ 4; -y ≤ -2; -x ≤ 0; -y ≤ 0. Solve graphically.
Coordinate-derived feasible-region graph for cbse12-math-lp-p1-short-009
Coordinate-derived feasible-region graph for cbse12-math-lp-p1-short-009

✅ Step-by-Step Solution

Final Answer: max Z=40 at (0,5).
  1. Draw each boundary ax+by=c and retain the closed half-plane ax+by≤c; intersect all constraints, including x,y≥0.
  2. Solving pairs of boundary equations and rejecting points violating any inequality gives vertices: (0,5), (3,2).
  3. Evaluate the objective at every vertex: (0,5) → 40; (3,2) → 31.
  4. The region is bounded. max Z=40 at (0,5).

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Draw each boundary ax+by=c and retain the closed half-plane ax+by≤c; intersect all constraints, including x,y≥0.
  • [1 mark] Solving pairs of boundary equations and rejecting points violating any inequality gives vertices: (0,5), (3,2).
  • [1 mark] Evaluate the objective at every vertex: (0,5) → 40; (3,2) → 31.
  • [0.5 marks] The region is bounded. max Z=40 at (0,5).

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