Question

The feasible region of an LPP is shown in the figure. If $z=3x+9y$, then the minimum value of $z$ occurs at

• A. $(5,5)$
• B. $(0,10)$
• C. $(0,20)$
• D. $(15,15)$

Answer 1

The correct option is A $(5,5)$

The corner points of the feasible region and the corresponding value of $z$ are
$$\begin{array}{cc}Points& z=3x+9y\\ A(15,15)& 3\times 15+9\times 15=180\\ B(0,20)& 3\times 0+9\times 20=180\\ C(0,10)& 3\times 0+9\times 10=90\\ D(5,5)& 3\times 5+9\times 5=60\end{array}$$
$\therefore z_{min}=60$ at $(5,5)$