NCERT Class 12 · Ch 12 Exercise 12.1 · Q4
NCERT Class 12 Maths · Chapter 12 Linear Programming · Exercise 12.1 Question 4
Minimize Z=3x+5y subject to x+3y≥3,x+y≥2,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: Minimum Z=7 at (3/2,1/2).
- Plot each boundary and intersect its indicated closed half-plane with x,y≥0.
- Solving boundary pairs and checking every inequality gives vertices (0,2), (3/2,1/2), (3,0).
- The objective values at these vertices are (0,2) → 10; (3/2,1/2) → 7; (3,0) → 9.
- The region is unbounded. Feasible recession directions are (0,1), (1,0), with objective changes 5, 3. Check these signs before declaring a finite optimum.
- Minimum Z=7 at (3/2,1/2).
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