Write Down (Without Solving) the Dual LP Problem $c = s + 6 t + u$

Multiple Choice

Write down (without solving) the dual LP problem.
Minimize $c = s + 6 t + u$ subject to
$$\begin{array} { l } 9 s - t + v \geq 3,000 \\u - v \geq 1,000 \\s + t \geq 500 \\s \geq 0 , t \geq 0 , u \geq 0 , v \geq 0\end{array}$$

A) maximize $$p = x + 6 y + z$$ subject to $$\begin{array} { l } 9 x - y + w \geq 3,000 \\z - w \geq 1,000 \\x + y \geq 500 \\x \geq 0 , y \geq 0 , z \geq 0 , w \geq 0\end{array}$$

B) maximize $p = 3,000 x + 1,000 y + 500 z$ subject to
$$\begin{array} { l } 9 x + z \geq 1 \\- x + z \geq 6 \\y \geq 1 \\x - y \geq 0 \\x \geq 0 , y \geq 0 , z \geq 0\end{array}$$

C) maximize $p = 3,000 x + 1,000 y + 500 z$ subject to

$$\begin{array} { l } 9 x + z \leq 1 \\- x + z \leq 6 \\y \leq 1 \\x - y \leq 0 \\x \geq 0 , y \geq 0 , z \geq 0\end{array}$$

D) maximize $p = x + 6 y + z$ subject to
$$\begin{array} { l } 9 x - y + w \leq 3,000 \\z - w \leq 1,000 \\x + y \geq 500 \\x \geq 0 , y \geq 0 , z \geq 0 , w \geq 0\end{array}$$

E) maximize $p = x + 6 y + z$ subject to

$$\begin{array} { l } 9 x + y + w \geq 3,000 \\z + w \geq 1,000 \\x + y \geq 500 \\x \geq 0 , y \geq 0 , z \geq 0 , w \geq 0\end{array}$$