NCERT Class 12 · Ch 12 Exercise 12.1 · Q5
NCERT Class 12 Maths · Chapter 12 Linear Programming · Exercise 12.1 Question 5
Maximize Z=3x+2y subject to x+2y≤10,3x+y≤15,x,y≥0. Solve graphically.
💡 Concept Hints
- Convert the inequalities to boundary lines and identify the common feasible region.
- Evaluate the objective at all feasible vertices, then check directions of escape if the region is unbounded.
✅ Step-by-Step Solution
Final Answer: Maximum Z=18 at (4,3).
- Plot each boundary and intersect its indicated closed half-plane with x,y≥0.
- Solving boundary pairs and checking every inequality gives vertices (0,0), (0,5), (4,3), (5,0).
- The objective values at these vertices are (0,0) → 0; (0,5) → 10; (4,3) → 18; (5,0) → 15.
- The region is bounded. The corner-point theorem applies. If two vertices share an optimal value, linearity gives the same value on their whole joining segment.
- Maximum Z=18 at (4,3).
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