Consider the inequalities x > y and x + y ≤ 3 where y ≤ 1. The feasible region is:

open half plane containing the point (2, 1)

Given inequalities

$x>y$

$x+y\le3$

$y\le1$

Check origin $(0,0)$

$0>0$ is false

So origin is not in region

Check point $(0,3)$

$y=3\le1$ is false

So not in region

Check point $(2,1)$

$2>1$ true

$2+1=3\le3$ true

$1\le1$ true

So $(2,1)$ lies in region

Since $x>y$ is strict inequality, region is open

Also region is not bounded

Correct answer: open half plane containing the point $(2,1)$