Consider the following model:

Minimize $=1+22$

subject to $21+2>=1$

$122>=1$

and $1>=0,2>=0.$

$($a$)[5$ points$]$ Construct the dual problem.

$($b$)[5$ points$]$ Use graphical analysis of the dual problem to determine whether the primal

problem has feasible solutions and, if so$,$ whether its objective function is bounded