• # question_answer For the following shaded area, the linear constraints except $x\ge 0$ and $y\ge 0$, are    A) $2x+y\le 2,\ x-y\le 1,\ x+2y\le 8$           B) $2x+y\ge 2,\ x-y\le 1,\ x+2y\le 8$ C) $2x+y\ge 2,\ x-y\ge 1,\ x+2y\le 8$         D) $2x+y\ge 2,\ x-y\ge 1,\ x+2y\ge 8$

To test the origin for $2x+y=2,x-y=1$ and $x+2y=8$in reference to shaded area, $0+0<2$is true for $2x+y=2$.  So for the region does not include origin (0, 0), $2x+y\ge 2$. Again for $x-y=1,\,0-0<1$, $\therefore \,\,\,\,x-y\le 1$ Similarly for $x+2y=8,0+0<8$;  \ $x+2y\le 8$.