(Solved): The initial simplex tableau of a linear programming problem is shown below. Answer parts (a) - (c). ...

The initial simplex tableau of a linear programming problem is shown below. Answer parts (a) - (c). \[ \left[\begin{array}{cccccc|c} x_{1} & x_{2} & x_{3} & s_{1} & s_{2} & z & \\ 1 & 1 & 1 & 1 & 0 & 0 & 12 \\ 3 & 1 & 3 & 0 & 1 & 0 & 39 \\ \hline-3 & -3 & -1 & 0 & 0 & 1 & 0 \end{array}\right] \] (a) Use the simplex method to solve the problem with column 1 as the first pivot column. Select the correct choice below and, necessary, fill in the answer box to complete your choice. A. The maximum is when \( x_{1}=, x_{2}=, x_{3}=, s_{1}= \) and \( s_{2}= \)