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GATE 2026 PI – Question 14

Operations Research and Operations Management · Operations Research · 1 mark · Multiple choice

Which option gives ALL constraints defining the feasible region shown? The figure is not to scale.

Diagram for GATE 2026 PI question 14
  1. $x_1,x_2\ge0;\ x_2\ge3;\ x_1-x_2\le1;\ x_1-0.5x_2\ge1$
  2. $x_1,x_2\ge0;\ x_2\le3;\ x_1-x_2\le1;\ x_1+0.5x_2\ge1$
  3. $x_1,x_2\ge0;\ x_2\le4;\ x_1-x_2\le1;\ x_1+0.5x_2\ge1$
  4. $x_1,x_2\ge0;\ x_2\le3;\ x_1+x_2\le1;\ x_1+0.5x_2\ge1$

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Correct answer: (B) $x_1,x_2\ge0;\ x_2\le3;\ x_1-x_2\le1;\ x_1+0.5x_2\ge1$

Explanation

The region is in the first quadrant below $x_2=3$. Its rising boundary joins (1,0) and (4,3), giving $x_1-x_2=1$; the region lies on the $\le1$ side. Its descending boundary joins (0,2) and (1,0), giving $x_1+0.5x_2=1$, with the region on the $\ge1$ side. These conditions give **B**.

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