Consider the following linear program with five constraints.

MINIMIZE $10$x $-$ y

subject to

x $<=4$ y $<=6$ x $+$ y $>=3$ x $>=2$ y $>=2$

We solve this graphically on a graph with x on the horizontal axis and y on the vertical axis.

Does a feasible region exist? If so$,$ what does it look like? Type the ONE DIGIT NUMBER corresponding to the correct answer.

$1$ There is no feasible region

$2$ It is a single point

$3$ It is a three$-$sided figure $($a triangle$)$

$4$ It is a four$-$sided figure $($a quadrilateral$)$

$5$ It is a five$-$sided figure $($a pentagon$)$