2007-II-43

Ans: B
The equation of the straight line passing through $(0,8)$ and $(4,0)$ is

$\begin{array}{rcl}{\displaystyle \frac{x}{4}}+{\displaystyle \frac{y}{8}}& =& 1\\ 2x+y& =& 8\end{array}$

Note that region II and IV are lying on the side $2x+y\ge 8$.

The equation of the straight line passing though $(0,8)$ and $(8,0)$ is

$\begin{array}{rcl}{\displaystyle \frac{x}{8}}+{\displaystyle \frac{y}{8}}& =& 1\\ x+y& =& 8\end{array}$

Note that region I, II, III and IV are lying on the side $x+y\le 8$.

The equation of the straight line passing though $(0,4)$ and $(4,4)$ is $y=4$.

Note that region I and II are lying on the side $y\ge 4$.

Hence, the required region is II.