b$.$

Solve the following linear programming problem graphically.

minimize $z=-3x_1$

subject $to$

$2x_1+x_{2}3$

$3x_1-x_{2}2$

$x_1+x_{2}1$

$x_1,x_{2}0$

c$.$

Consider the same linear programming problem provided in Part b$,$ except for the objective function. Let the new objective function be minimize $0\mathrm{.}5x_1+0\mathrm{.}5x_2.$ Solve the problem and define the characteristic of the optimal solution. Does the optimal value change as the optimal solution changes?