Consider the following linear programming problem:

Max$$x$1+2$x$2$

$$ s$.$t$.$x$1+$x$23$

$$ x$1-2$x$20$

$$x$21$

$$x$1,$x$20$

$$

a$.$ Identify the feasible region. $(12$ points$)$

b$.$ Are any of the constraints redundant?$$ If yes, then identify the constraint that is redundant. $(10$ points$)$

c$.$ Find all the extreme points $$ list the value of x$1$ and x$2$at each extreme point. $(6$ points$)$

d$.$ What is the optimal solution? $(5$ points$)$