Consider the following linear programming problem:

Max $x_1+2x_2$

$s.t.x_1+x_{2}3$

$x_1-2x_{2}0$

$,x_{2}1$

$,x_1,x_{2}0$

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$)$

Question $13(25$ points$)$