NCERT Class 12 Maths · Chapter 12 Linear Programming · Exercise 12.1 Question 6

Question

Minimize Z=x+2y subject to 2x+y≥3,x+2y≥6,x,y≥0. Show that the minimum occurs at more than two points. Solve graphically.

Accepted Answer

Final Answer: Minimum Z=6 at (0,3), (6,0) and every point of the segment joining these vertices. Step 1: Plot each boundary and intersect its indicated closed half-plane with x,y≥0. Step 2: Solving boundary pairs and checking every inequality gives vertices (0,3), (6,0). Step 3: The objective values at these vertices are (0,3) → 6; (6,0) → 6. Step 4: The region is unbounded. Feasible recession directions are (0,1), (1,0), with objective changes 2, 1. Check these signs before declaring a finite optimum. Step 5: Minimum Z=6 at (0,3), (6,0) and every point of the segment joining these vertices.

NCERT Class 12 Maths · Chapter 12 Linear Programming · Exercise 12.1 Question 6

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