Question

The point $(2,1)$ lies in the _____ region of the solution of linear inequations $x-2y\le 0,$ and $x-y>0$

• A. feasible
• B. non-feasible
• C. unbounded
• D. bounded

Answer 1

Answer: (A), (C)

unbounded
feasible

Given, $x-2y\le 0$ and

$x-y>0⟹x>y⟹y<x$

First draw the graph for the equations, $x-2y=0$ and

$y=x$

$x-2y=0$ and $y=x$ are the lines which pass through the origin as shown in the above fig.

Hence, $y<x$ includes the below region of the line and

$x-2y\le 0$ also includes the below region of the line.

Therefore, the blue shaded region is the feasible region which is unbounded.

Given point (2,1). Substituting in the given inequations,

$x-2y\le 0⟹2-2\ast 1\le 0⟹0\le 0$ True

$x-y>0⟹2-1>0⟹1>0$ True

Therefore, (2,1) belongs to the feasible region which is unbounded.