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Math Help - Criterion Function, corner points

  1. #1
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    Criterion Function, corner points

    The Function z=f(x,y)=11x+12y

    Constraints: (>=greater or equal to, >=less than or equal to)
    x>0,
    y>0,
    x+y>11,
    y<x+12,
    y<14,
    x-y<11

    What are the corner points? I don't even know where to begin
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  2. #2
    A Plied Mathematician
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    To plot a single inequality, such as x+y > 11, how would you go about it?
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  3. #3
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    To be honest I have no idea, I missed this lecture last week. Maybe I'm just overanalyzing it though.
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  4. #4
    A Plied Mathematician
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    To plot x + y > 11, perform the following steps:

    1. Solve for y in the equation x + y = 11, if you can. Answer: y = - x + 11.
    2. Plot the equation version of the inequality.
    3. The solution to the inequality is going to be either the half-plane on one side of the equation's plot, or the other. To determine which one is correct, plug in a point that is not on the line, for example, (1,0), and see if it satisfies the inequality. If it does, then the half-plane containing that point is the solution. Otherwise, the other half-plane is the solution.

    Does that make sense? This procedure, incidentally, works for any proper function. You just won't have clean half-planes to deal with; you'll have regions of the plane to deal with.
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  5. #5
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    That makes a lot of sense, Thanks for your help.
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  6. #6
    A Plied Mathematician
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    You're welcome. Have a good one!
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