Consider a linear program over constraint set x1 + x2 2 -x1 + x2 0

Consider a linear program over constraint set x1 + x2 Ú 2

-x1 + x2 Ú 0 x2 … 2 x1, x2 Ú 0

(a) Identify the feasible set in a 2-dimensional plot.

(b) Devise a linear objective function for which the LP has a unique optimal solution, and illustrate graphically.

(c) Devise a linear objective function for which the LP has alternative optimal solutions, and illustrate graphically.

(d) Devise a linear objective function for which the LP is unbounded, and illustrate graphically.

(e) Propose a constraint which, if added to the above constraints, would make the problem infeasible, and illustrate graphically.