Question

The region represented by the inequalities
$ x \ge 6, y \ge2, 2 x + 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 $
$l_3 : 2 x + y = 10$
$l_4 : x = 0$
and $l_5 : y = 0$
The graph of the inequalities $2 x + y \le 10$,
$y \ge 2, x \ge 0, y \ge 0$ 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.