Solve the following linear programming $($LP$)$ problem using Graphical method:

Maximize $Z=5x1+7x2$

Subject $to$:

$2x1+3x218$

$x1+x2=8$

$x24$

and $x10,x20$

a$-$ Plot the feasible region

b$-$ Determine all corner point feasible solutions,

c$-$ Determine all basic feasible solutions,

d$-$ Determine all optimal solutions,