Solve the Standard Minimization Problem Using Duality $c = 4 s + t + 7 u$

Short Answer

Solve the standard minimization problem using duality.
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Minimize $c = 4 s + t + 7 u$ ​
subject to $$\begin{aligned}s + t + u & \geq 50 \\2 s + t & \geq 25 \\t + u & \geq 25 \\s \geq 0 , t \geq 0 , u & \geq 0\end{aligned}$$ ​ $c =$ _________
​ $s =$ _________
​ $t =$ __________
​ $u =$ __________