Minimize $c = 5 x + y + z + 2 w$

Multiple Choice

Minimize $c = 5 x + y + z + 2 w$
Subject to
$$\begin{aligned}5 x - y + w & \geq 1,000 \\z + w & \leq 2,000 \\x + y & \leq 500 \\x \geq 0 , y \geq 0 , z \geq 0 , w & \geq 0\end{aligned}$$

A) $c = 600$ , $x = 0$ , $y = 200$ , $z = 200$ , $w = 200$
B) $c = 1,600$ , $x = 200$ , $y = 200$ , $z = 200$ , $w = 200$
C) $c = 1,000$ , $x = 200$ , $y = 0$ , $z = 0$ , $w = 0$
D) $c = 200$ , $x = 0$ , $y = 200$ , $z = 0$ , $w = 0$
E) no solution