$4\mathrm{.}1-6.$ Describe graphically what the simplex method does step by step to solve the

following problem.

Maximize

subject $to$

$-3x_1+x_{2}1$

$4x_1+2x_{2}20$

$4x_1-x_{2}10$

$-x_1+2x_{2}5$

Maximize $,Z=2x_1+3x_2,$

subject to

$-3x_1+x_{2}1$

$4x_1+2x_{2}20$

$4x_1-x_{2}10$

$-x_1+2x_{2}5$

and

$x_{1}0,x_{2}0.$