Ans: D
Note that the shaded region represents the solution of $\left\{\begin{array}{rcl}
y & \le & 6-2x \\
y & \le & x+3 \\
y & \ge & 3
\end{array}\right.$.
Note that the shaded region represents the solution of $\left\{\begin{array}{rcl}
y & \le & 6-2x \\
y & \le & x+3 \\
y & \ge & 3
\end{array}\right.$.
I is true. By the third inequality, the $y$ coordinates of all point in the shaded region is greater than or equal to $3$. i.e. $k\ge 3$.
II is true. By the second inequality, we have
$\begin{array}{rcl}
k & \le & h + 3 \\
h-k & \ge & -3
\end{array}$
III is true. By the first inequality, we have
$\begin{array}{rcl}
k & \le & 6-2h \\
2h + k & \le & 6
\end{array}$
