$5.(12$ points$)(20$ minutes$)$

Consider the following LP:

$=++$

s$.$t$.$

$++<=$

$++<=$

$,,>=$

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$)$