Consider the following linear program and solve questions, $1.$ a$)-1.$ c$).$

Max,$x1+x2$

$s.t.x1+x25$

$,x1+3x23$

$x10$ and $x20$

a$)$ Graph the feasible set.

b$)$ Find all corner point feasible solutions $($CFS$).$

c$)$ What is the optimal solution.