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Thread: dual problem formulation??

  1. #1
    Oct 2007

    dual problem formulation??

    Maximise Z = 2X1 + X2

    subject to:

    X1 + 3X2 <= 25
    3X1 + 3X2 = 15
    2X1 + X2 >= 4

    X1, X2 >= 0
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  2. #2
    Dec 2007
    You can solve this by gaphical method, i.e.
    1. You plot the constraints,taking x1 as x and x2 as y, {feasible region)
    2. plot the objective fcn using two different values of z, (iso-lines)
    3. observe the direction of 2. as z increases
    4. Find out the last point(may also be a segment) in the feasible region which will be touched by an iso line.

    if you do this, you'll notice that you're feasible region is a line (the second constraint). The last point of that line that will be touched by the iso lines (iso-lines are actually parallel to the third constraint and it is actually heading towards the direction of the origin) is the point (0,5). This gives you the maximum z=5.

    You can also use simplex method but that entails more time and effort. Since your problem involves only two variables, it's much easier to graph.
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