1. The Fundamental Theorem of Linear Programming says that if an LP is feasible it has a BFS; additionally, if it has an optimal solution, it has an optimal BFS. Consider the LP: maximize z = 0 x1 + 0 x2 s.t. (x1, x2) <2 .

(a) Is this LP feasible or infeasible? Justify your answer.

(b) Does the LP have an optimal solution? Justify your answer.

(c) Does the LP have a BFS? If yes, give one; if no, how can you reconcile this with the Fundamental Theorem of Linear Programming?

(d) Is the feasible solution-set of the LP a polyhedron? Justify your answer.