Mathbee CBSE Mathbee · CBSE Class 12 Maths
Class 12 Linear Programming · Long Answer3 Marksgraphical_optimization

Class 12 Maths · Linear Programming · Long Answer #36

Maximize Z=20*x + 10*y subject to 3*x + 6*y ≤ 84; 3*x + y ≤ 24; -x ≤ 0; -y ≤ 0. Solve graphically.
Coordinate-derived feasible-region graph for cbse12-math-lp-p1-short-010
Coordinate-derived feasible-region graph for cbse12-math-lp-p1-short-010

✅ Step-by-Step Solution

Final Answer: max Z=200 at (4,12).
  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: (0,0), (0,14), (4,12), (8,0).
  3. Evaluate the objective at every vertex: (0,0) → 0; (0,14) → 140; (4,12) → 200; (8,0) → 160.
  4. The region is bounded. max Z=200 at (4,12).

📋 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: (0,0), (0,14), (4,12), (8,0).
  • [1 mark] Evaluate the objective at every vertex: (0,0) → 0; (0,14) → 140; (4,12) → 200; (8,0) → 160.
  • [0.5 marks] The region is bounded. max Z=200 at (4,12).

Master Chapter 12: Linear Programming

Practise interactive questions, flashcards, visual mind maps, and timed board tests for Linear Programming.
📘 Chapter Notes & All Exercises 🚀 Open in Interactive Workspace →
← Previous Question
Maximize Z=5*x + 8*y subject to x + y ≤ 5; -x - y ≤ -5; x ≤ 4; -y ≤…
Next Question →
Maximize Z=22*x + 18*y subject to 3*x + 2*y ≤ 48; x + y ≤ 20; -x ≤…

More Practice Questions in Linear Programming

Q1Q2Q3Q4Q5Q6Q7Q8Q9Q10Q11Q12Q13Q14Q15Q16Q17Q18Q19Q20Q21Q22Q23Q24Q25Q26Q27Q28Q29Q30Q31Q32Q33Q34Q35Q36Q37Q38Q39Q40

Related Questions in Linear Programming

Class 12 Linear Programming · Mcq Single Correct
How many feasible solutions satisfy 3x+y≤12, x+2y≤10, x,y≥0?
Class 12 Linear Programming · Mcq Single Correct
The shaded first-quadrant region lies above both x+2y=4 and x+y=3. Which constraints describe…
Class 12 Linear Programming · Mcq Single Correct
Z=ax+by has maximum 42 at (4,6) and minimum 19 at (3,2). Find a,b.
Class 12 Linear Programming · Mcq Single Correct
A bounded feasible polygon has vertices (2,72),(15,20),(40,15). For Z=18x+9y, select the…
Class 12 Linear Programming · Mcq Single Correct
How many vertices does x−y≥0, 2y≤x+2, x,y≥0 have?
Class 12 Linear Programming · Mcq Single Correct
A bounded feasible polygon has vertices (0,3),(3,2),(0,5). Find the minimum of Z=11x+7y.