$(20)$ Consider the following

MAXZ$=2x_1+4x_2+3x_3+x_4$

$s.t$

$3x_1+x_2+x_3+4x_{4}12$

$x_1-3x_2+2x_3+3x_{4}7$

$2x_1+x_2+3x_3-x_{4}10$

$x_{i}0$

The optimal solution of this $LP$:$x1=0$;$x2=10\mathrm{.}4$;$x3=0$;$x4=0\mathrm{.}4$

a$.$ Find the dual of the $LP.$

b$.$ Using optimal solution and complementary slackness conditions, Find the solution of the dual model and prove that the solution is optimal.