(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. 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

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# Homework Help: Linear programming proofs PLEASE HELP!

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