Class 12 Linear Programming · Long Answer3 Marksgraphical_optimization
Class 12 Maths · Linear Programming · Long Answer #58
Find max Z=3x+2y on the bounded polygon with vertices (0,0),(0,8),(2,7),(5,4),(6,0).
✅ Step-by-Step Solution
Final Answer: 23 at (5,4).
- Use the corner-point theorem for the bounded feasible polygon.
- Evaluate Z: (0,0)→0; (0,8)→16; (2,7)→20.
- At (5,4), Z=15+8=23; at (6,0), Z=18.
- The maximum is 23 at (5,4).
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Use the corner-point theorem for the bounded feasible polygon.
- [1 mark] Evaluate Z: (0,0)→0; (0,8)→16; (2,7)→20.
- [1 mark] At (5,4), Z=15+8=23; at (6,0), Z=18.
- [0.5 marks] The maximum is 23 at (5,4).
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