Question

The shaded part of given figure indicates the feasible region

then the constraints are

• A. $x,y\ge 0,x+y\ge 0,x\ge 5,y\le 3$
• B. $x,y\ge 0,x-y\ge 0,x\le 5,y\le 3$
• C. $x,y\ge 0,x-y\ge 0,x\le 5,y\ge 3$
• D. $x,y\ge 0,x-y\le 0,x\le 5,y\le 3$

Answer 1

Answer: (B)

In the given figure, we see that $OC$ line
passing through (0,0) and (3,3) .
$\therefore$ Equation of line is $y=x$
Also, we see that shaded portion of this line is towards the $X$ -axis, so we take $x-y\ge 0$.
In the figure, line $AB$ is parallel to $Y$ -axis.
$\therefore$ Equation of line $AB$ is $x=5$, also shaded portion of this line is towards the origin, so we take $x-5\le 0$ or $x\le 5$
In the figure, line $BC$ is parallel to $X$ -axis
$\therefore$ Equation of line $BC$ is $y=3$. Also, shaded
portion of this line is towards the origin, so we take $y-3\le 0$ or $y\le 3$
Also, the shaded region lies in first quadrant, so $x\ge 0$ and $y\ge 0$
Hence, constraints of given shaded region are
$x,y\ge 0,x-y\ge 0,x\le 5,y\le 3$