(Solved): linear programming-duals and simplex method Find the dual of the following linear program (do not so ...

Find the dual of the following linear program (do not solve). Minimize \( z=4 x_{1}+4 x_{2}+6 x_{3} \) subject to \[ \begin{array}{l} x_{1}-x_{2}-x_{3} \leq 3 \\ x_{1}-x_{2}+x_{3} \geq 3 \\ x_{1} \geq 0, x_{2} \geq 0, x_{3} \geq 0 \\ \text { Maximize } w=3 y_{1}-3 y_{2} \text { subject } \\ \text { to } \\ y_{1}+y_{2} \leq 4 \\ y_{1}-y_{2} \leq 4 \\ y_{1}+y_{2} \leq 6 \\ y_{1} \geq 0, y_{2} \geq 0 \\ \text { Maximize } w=-3 y_{1}+3 y_{2} \text { subject } \\ \text { to } \\ -y_{1}+y_{2} \leq 4 \\ y_{1}-y_{2} \leq 4 \\ y_{1}+y_{2} \leq 6 \\ y_{1} \geq 0, y_{2} \geq 0 \end{array} \] Maximize \( W=3 y_{1}-3 y_{2} \) subject to \( -3 y_{1}+y_{2} \leq 4 \) \( y_{1}-y_{2} \leq 4 \) \( y_{1}-y_{2} \leq 6 \) \( y_{1} \geq 0, y_{2} \geq 0 \) Maximize \( w=-y_{1}+3 y_{2} \) subject to \( -3 y_{1}+y_{2} \leq 4 \) \( y_{1}-y_{2} \leq 4 \) \( y_{1}+y_{2} \leq 6 \) \( y_{1} \geq 0, y_{2} \geq 0 \) Maximize \( w=-3 y_{1}+3 y_{2} \) subject to \( -y_{1}+y_{2} \leq 4 \) \( -y_{1}-y_{2} \leq 4 \) \( y_{1}-y_{2} \leq 6 \) \( y_{1} \geq 0, y_{2} \geq 0 \)