Consider the following problem:

max,$x_1+2x_2$

$s.t.$: $x_1-x_{2}2$

$,4x_1+x_{2}4$

$,x_1,x_{2}0$

a$)$ Demonstrate graphically that this problem is infeasible.

b$)$ Construct the dual problem.

c$)$ Demonstrate graphically that the dual problem is unbounded.