(Solved): Consider the linear program: Minimize \( z=2 x_{1}+x_{2} \), subject to: \[ \begin{array}{r} -4 x_ ...

Consider the linear program: Minimize \( z=2 x_{1}+x_{2} \), subject to: \[ \begin{array}{r} -4 x_{1}+3 x_{2}-x_{3} \geq 16, \\ x_{1}+6 x_{2}+3 x_{3} \geq 12, \\ x_{i} \geq 0 \quad \text { for } i=1,2,3 . \end{array} \] a) Write the associated dual problem. b) Solve the primal problem, using the dual simplex algorithm. c) Utilizing the final tableau from part (b), find optimal values for the dual variables \( y_{1} \) and \( y_{2} \). What is the corresponding value of the dual objective function?