Question

The region represented by the inequation system $x,y\ge 0$, $y\le 6,$ $x+y\le 3$ is

• A. unbounded in the first quadrant
• B. unbounded in first and second quadrants
• C. bounded in the first quadrant
• D. None of the above

Answer 1

The correct option is C

bounded in the first quadrant

Explanation for the correct answer:

Compute the quadrant:

The line $y=6$ is a line parallel to the $x$ axis at a distance of $6$ units.

The line $x+y=3$ intersects both the $x$ and $y$ axis.

Their intercepts are found as

Substitute $x=0$

$\Rightarrow y=3$

Substitute $y=0$

$\Rightarrow x=3$

$\therefore$ $\left(3,0\right)$ and $\left(0,3\right)$ are the intercepts cut by the line

Thus the region bounded by inequalities can be drawn as

From the figure, it can be deduced that the region is bounded in the first quadrant.

Hence, option $\left(C\right)$ is the correct answer.