$4\mathrm{.}6-10.*$ Consider the following problem.

Maximize $Z=-x_1+4x_2,$

subject to

$-3x_1+x_2,6$

$x_1+2x_2,4$

$x_2,-3$

$($no lower bound constraint for $x_1).$

D$,$I $($a$)$ Solve this problem graphically.

$($b$)$ Reformulate this problem so that it has only two functional constraints and all variables have nonnegativity constraints.

D$,$I $($c$)$ Work through the simplex method step by step to solve the problem.