Question: Write the general dual of the following problem. [ begin{array}{l} operatorname{minimize} z=3 x_{1}+2 x_{2} quad 4 x_{3} text { subject to } begin{array}{l}

Write the general dual of the following problem. \[ \begin{array}{l} \operatorname{minimize} z=3 x_{1}+2 x_{2} \quad 4 x_{3} \\ \text { subject to } \\ \begin{array}{l} 5 x_{1}-7 x_{2}+x_{3} \geq 12 \\ x_{1}-x_{2}+2 x_{3}=18 \\ 2 x_{1}-x_{3} \leq 6 \\ x_{1}, x_{2}, x_{3} \geq 0 \end{array} \end{array} \]

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