NCERT Class 12 Maths · Chapter 12 Linear Programming · Exercise 12.1 Question 8

✅ Step-by-Step Solution

1. Plot each boundary and intersect its indicated closed half-plane with x,y≥0.
2. Solving boundary pairs and checking every inequality gives vertices (0,50), (0,200), (20,40), (50,100).
3. The objective values at these vertices are (0,50) → 100; (0,200) → 400; (20,40) → 100; (50,100) → 250.
4. 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.
5. Minimum Z=100 at (0,50), (20,40) and every point of the segment joining these vertices. Maximum Z=400 at (0,200).