$(12$ points$)(20$ minutes$)$

Consider the following LP:

maxz$=5x_1+3x_2+x_3$

$s.t.$

$2x_1+x_2+x_{3}6$

$x_1+2x_2+x_{3}7$

$x_1,x_2,x_{3}0$

a$)(4$ points$)$ Take the dual of this LP

b$)(4$ points$)$ Graphically solve the dual of this LP$.$

c$)(4$ points$)$ Then use complementary slackness to solve the max problem $($Primal LP$).$