Problem $2$

Consider the following problem:

Maximize $z=3x_1+2x_2+5x_3$

Subject to:

$3x_1+2x_2+x_{3}12$

$2x_1+3x_2+2x_{3}15$

$x_1+x_2-x_{3}3$

$x_1,x_2,x_{3}0$

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.