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Thread: [SOLVED] linear programming problem..

  1. #1

    Red face [SOLVED] linear programming problem..

    Question 1:
    Determin values for X and Y as will: Maximize 8X + 11Y
    Subject to:
    3X + 2Y <= 12
    4X + 7Y <= 28
    Y >= 0
    X >= 0

    Question 2:
    X and Y are now to be integer, so the (X,Y) combinations that approximate continuous solution are : (3,3),(2,3),(2,2),(3,2) which of these are a feasible solution to a new integer programming problem?

    is (X=2, Y=2) the optimal solution to the interger programming problem?
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  2. #2
    MHF Contributor
    Aug 2007
    Since this is a two-variable problem, the solution can be performed graphically or algebraically. Where do the two constraints meet? I get (28/13,36/13). A quick check of the graph show this a nice solution. Add y = (-8/11)x + (620/143) to your graph.

    For #2, simply check which points are in the feasable region. Anything outside ANY constraint is no good.
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