Is the Set C Nonempty and Unbounded for Given Linear Programming Constraints?

[csc2iffy]

Homework Statement

Let C be the set of all points (x,y) in the plane satisfying x≥0, y≥0, -x-2y≤-8.

a. Show that C is nonempty and unbounded.
b. Prove that the LP problem: Max M=2x+3y subject to the constraint that (x,y) lie in C has no feasible, optimal solution.
c. Show that the LP problem: Max M=-3x-6y subject to the constraint that (x,y) lie in C does have a feasible, optimal solution.

Homework Equations

The Attempt at a Solution

a. I graphed the constraints and showed that the feasible region is the entire first quadrant, and therefore C is nonempty and unbounded (provided attachment of my work - is this enough?)

b. I could "show" this but I have no idea how to "prove" it. Does it involve the simplex method?

c. Same question as above

 

[ehild]

You plotted the wrong line in the figure.It should be -x-2y=-8.

As for b and c: It is a good start to show. Do it.

ehild