Question

The region represented by the inequalities
$x\ge 6,y\ge 2,2x+y\le 10,x\ge 0,y\ge 0$ is

• A. unbounded
• B. a polygon
• C. a triangle
• D. None of these

Answer 1

Answer: (D)

Let $l_1:x=6$
$l_2:y=2$
$l_3:2x+y=10$
$l_4:x=0$
and $l_5:y=0$
The graph of the inequalities $2x+y\le 10$,
$y\ge 2,x\ge 0,y\ge 0$ is
the region bounded by $\Delta BCD$. This region has no point in common with the region $x\ge 6,y\ge 2$ as is clear from the figure. Hence, the region of the given inequalities is an empty set.