$4\mathrm{.}4-6.$ Consider the following problem.

Maximize $Z=3x_1+5x_2+6x_3,$

subject to

$2x_1+x_2+x_{3}4$

$x_1+2x_2+x_{3}4$

$x_1+x_2+2x_{3}4$

$x_1+x_2+x_{3}3$

and

$x_{1}0,x_{2}0,x_{3}0.$

D$,$I $($a$)$ Work through the simplex method step by step in algebraic form.

D$,$I $($b$)$ Work through the simplex method in tabular form.

C $($c$)$ Use a computer package based on the simplex method to solve the problem.