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Math Help - Help with complex systems of equations

  1. #1
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    Help with complex systems of equations

    Hi All
    These equations are the resulte from a lagrange multiplier optimization problem. I can not get the algebra right! Please help!

    280*pi*r + 80*pi*hi - 2*lamda*r*h = 0
    80*pi*r - lamda*pi*r^2=0
    -pi*r^2*h + 100=0
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  2. #2
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    Re: Help with complex systems of equations

    Quote Originally Posted by DanielLiwicki View Post
    Hi All
    These equations are the resulte from a lagrange multiplier optimization problem. I can not get the algebra right! Please help!

    280*pi*r + 80*pi*hi - 2*lamda*r*h = 0
    80*pi*r - lamda*pi*r^2=0
    -pi*r^2*h + 100=0
    What is hi?

    CB
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  3. #3
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    Re: Help with complex systems of equations

    pi not hi ....sorry
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  4. #4
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    Re: Help with complex systems of equations

    Lagrange multiplier problems typically give something like f(x,y,z)= \lambda g(x,y,z), h(x,y,z)= \lambda k(x,y,z), etc. I have found that it is often best to divide one equation by another, immediately eliminating \lambda (which is not part of the solution, any way).

    Here, you have 40\pi(7r+ \pi)= 2\lambda r h and 80\pi r= \lambda \pi r^2
    Dividing the first equation by the second,
    \frac{7r+ \pi}{2r}= \frac{2h}{r}
    so that 7r+ \pi= 4h.

    You can solve that for either r or h in terms of the other and put into the final equation.

    (Are you sure about the "hi= pi"? It seems strange that you would write "pi*pi" rather than "pi^2" and also strange that "pi^2" would show up in such a problem.)
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  5. #5
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    Re: Help with complex systems of equations

    Your Right!!! Not hi...not pi... but just h.
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  6. #6
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    Re: Help with complex systems of equations

    So you have 7r+ h= 4h.
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  7. #7
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    Re: Help with complex systems of equations

    It worked out! Thank you!
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