Minimize $P = 18 x + 4 y$ Subject to the Given Constraints

Multiple Choice

Minimize $P = 18 x + 4 y$ subject to the given constraints.
$\left\{\begin{array}{rll}x & \geq & 0 \\y & \geq & 0 \\x+4 y & \geq & 9 \\4 x+y & \geq & 9\end{array}\right.$

A) $\quad P = 99$ at $( 4.5,4.5 )$
B) $\quad P = 9$ at $( 0,4 )$
C) $\quad P = - 72$ at $( - 4,0 )$
D) $\quad P = 36$ at $( 0,9 )$
E) none of these