Q1: Suppose that the following constraints have been provided for a linear programming model.

(1)

(2)

and

.

a) Demonstrate that the feasible region is unbounded.

b) If the objective is to maximize

, does that model have an optimal soultion? If so, find it. If now, explain why not.

c) Repeat part (b) when the objective is to maximize

.

Does "unbounded" mean something specific when dealing with LP problems? When, I graph the above lines, I am not sure where the feasible region is, since the inequality tells me to shade below both lines in the first quadrant. Furthermore, since line (2) is above line (1) I have to shade over line (1) down to the horizontal axis, which doesn't seem right, as that would mean the constraints are not being satisfied. Does this mean the the feasible region is unbouned? Also,

Moreover, if the feasible region is unbouned and the gradiants of both objective functions from parts (b) and (c) are in directions away from the first quadrant, how can there be optimal solutions?