(Solved): PROBLEM 2 (20 points): Solve the following linear program using the Simplex Algorithm (note that o ...

PROBLEM 2 (20 points): Solve the following linear program using the Simplex Algorithm (note that one variable has unrestricted sign) Maximize \( z=x_{1}+6 x_{2} \) Subject to \( x_{1}+4 x_{2} \leq 6 \) \[ \begin{array}{l} -2 x_{1}-x_{2} \leq 2 \\ \quad x_{1} \text { u.r.s, } x_{2} \geq 0 \end{array} \]