(Solved): The initial tableau of a linear programming problem is given. Use the simplex method to solve the p ...

The initial tableau of a linear programming problem is given. Use the simplex method to solve the problen \[ \left[\begin{array}{rrrrrrr} x_{1} & x_{2} & x_{3} & s_{1} & s_{2} & z & \\ 1 & 4 & 6 & 1 & 0 & 0 & 14 \\ 2 & 1 & 5 & 0 & 1 & 0 & 24 \\ \hline-3 & -1 & -2 & 0 & 0 & 1 & 0 \end{array}\right] \] The maximum is when \( x_{1}=, x_{2}=, x_{3}=, s_{1}= \), and \( s_{2}= \) (Type integers or simplified fractions.)