$3-11.$ Consider the following LP:

Maximize $z=2x_1+3x_2$

subject to

$x_1+3x_{2}6$

$3x_1+2x_{2}6$

$x_1,x_{2}0$

$($a$)$ Express the problem in equation form.

$($b$)$ Determine all the basic solutions of the problem, and classify them as feasible

and infeasible.

$*($c$)$ Use direct substitution in the objective function to determine the optimum

basic feasible solution.

Note: Equation form is standard form