Write Down (Without Solving) the Dual LP Problem $p = x + y + z + w$

Write down (without solving) the dual LP problem.
Maximize $p = x + y + z + w$ subject to
$$\begin{array} { l } x + y + z \leq 9 \\y + z + w \leq 7 \\x + z + w \leq 2 \\x + y + w \leq 4 \\x \geq 0 , y \geq 0 , z \geq 0 , w \geq 0\end{array}$$

A) minimize $c = 9 s + 7 t + 2 u + 4 v$ subject to $$\begin{array} { l } s + u + v \leq 1 \\s + t + v \leq 1 \\s + t + u \leq 1 \\t + u + v \leq 1 \\s \geq 0 , t \geq 0 , u \geq 0 , v \geq 0\end{array}$$

B) minimize $c = s + t + u + v$ subject to
$$\begin{array} { l } s + t + u \leq 7 \\t + u + v \leq 6 \\s + u + v \leq 3 \\s + t + v \leq 4 \\s \geq 0 , t \geq 0 , u \geq 0 , v \geq 0\end{array}$$

C) minimize $c = s + t + u + v$ subject to $$\begin{array} { l } s + t + u \geq 9 \\t + u + v \geq 7 \\s + u + v \geq 2 \\s + t + v \geq 4 \\s \geq 0 , t \geq 0 , u \geq 0 , v \geq 0\end{array}$$

D) minimize $c = s + t + u + v$ subject to

$$\begin{array} { l } s + t + u \geq 9 \\t + u + v \geq 7 \\s + u + v \geq 2 \\s + t + v \geq 4 \\s \geq 0 , t \geq 0 , u \geq 0 , v \geq 0\end{array}$$

E) minimize $c = 9 s + 7 t + 2 u + 4 v$ subject to
$$\begin{array} { l } s + u + v \leq 1 \\s + t + v \leq 1 \\s + t + u \leq 1 \\t + u + v \leq 1 \\s \geq 0 , t \geq 0 , u \geq 0 , v \geq 0\end{array}$$

Correct Answer:

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