The corner points of the feasible region in the graphical representation of a linear programming problem are $(2, 72)$, $(15, 20)$ and $(40, 15)$. If $z = 18x + 9y$ be the objective function, then : (a) $z$ is maximum at $(2, 72)$, minimum at $(15, 20)$ (b) $z$ is maximum at $(15, 20)$, minimum at $(40, 15)$ (c) $z$ is maximum at $(40, 15)$, minimum at $(15, 20)$ (d) $z$ is maximum at $(40, 15)$, minimum at $(2, 72)$