Minimize $P = 16 x + 2 y$ Subject to the Given Constraints

Multiple Choice

Minimize $P = 16 x + 2 y$ subject to the given constraints.
$\left\{\begin{aligned}x & \geq 0 \\y & \geq 0 \\x+2 y & \geq 8 \\2 x+y & \geq 8\end{aligned}\right.$

A) $\quad P = 72$ at $( 4,4 )$
B) $\quad P = 16$ at $( 0,8 )$
C) $\quad P = 8$ at $( 0,2 )$
D) $\quad P = - 32$ at $( - 2,0 )$
E) none of these