Solve the Standard Minimization Problem Using Duality $c = 6 s + 2 t$

question 131

Essay

Solve the standard minimization problem using duality.

Minimize $c = 6 s + 2 t$
subject to $$\begin{array} { l } s + t \geq 9 \\6 s + t \geq 24 \\s \geq 0 , t \geq 0\end{array}$$
After using the simplex method for dual problem to arrive at the tableau below, what is the maximum value for c
$\quad \quad x\quad y\quad z \quad w \quad c$
$\left[ \begin{array} { c c c c c } 0&1&\frac{1}{5}&\frac{1}{-5}&0\\\frac{4}{5}\\1&0&\frac{1}{-5}&\frac{6}{5}&0\\\frac{6}{5}\\0&0&3&6&1\\30\end{array} \right]$

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