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

Maximize $Z=36x1+40x2$

Subject $to$:

$3x1+5x245$

$x110$

$x28$

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,