Consider the following problem:

Minimize $z=-2x_1-x_2+x_3$

Subject to:

$x_1+x_{3}1$

$x_2+x_{3}1$

$x_1+x_2+x_3\frac{1}{2}$

$x_1,x_2,x_{3}0$

Solve this problem using the two$-$phase method

Clearly identify each phase and iteration.

Report the optimal solution and its objective function value,

if it exists.