$2$ Use the simplex algorithm to solve the following LP:

maxz$=2x_1+3x_2$

$s.t.x_1+2x_{2}6$

$2x_1+x_{2}8$

$x_1,x_{2}0$

$3$ Use the simplex algorithm to solve the following

problem:

maxz$=,2x_1-x_2+x_3$

$s.t.3x_1+x_2+x_{3}60$

$,$

$2x_1+x_2+2x_3,20$

$2x_1+2x_2+x_3,20$

$x_1,x_2,x_3,0$