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Homework Help: Linear programming proofs PLEASE HELP!

  1. Feb 9, 2012 #1
    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
     

    Attached Files:

  2. jcsd
  3. Feb 10, 2012 #2

    ehild

    User Avatar
    Homework Helper

    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
     
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