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Math Help - Lagrange Multipliers

  1. #1
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    Lagrange Multipliers

    Use Lagrange multipliers to find three positive numbers whose sum is 15 and whose product is as large as possible.


    Help please~~
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  2. #2
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    Quote Originally Posted by CandyKanro View Post
    Use Lagrange multipliers to find three positive numbers whose sum is 15 and whose product is as large as possible.


    Help please~~
    Let  x_1, x_2 , x_3 be the numbers:

    f = x_1 x_2 x_3 - \lambda(x_1 + x_2 +x_3 - 15)

    So you will get three conditions from this, x_2 x_3 = x_1 x_3 = x_1 x_2 = \lambda. This yields x_1 = x_2 = x_3 using the fact thay are positive. Substituting in the constaint yields x_1 = x_2 =x_3 = 5. Thus the maximum value is of product is 5^3

    (Note that I did not add the constraint that they are positive, and the answer turned out to be positive... so no problem with that)
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  3. #3
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    Quote Originally Posted by Isomorphism View Post
    So you will get three conditions from this, x_2 x_3 = x_1 x_3 = x_1 x_2 = \lambda. This yields x_1 = x_2 = x_3 using the fact thay are positive. Substituting in the constaint yields x_1 = x_2 =x_3 = 5. Thus the maximum value is of product is 5^3

    (Note that I did not add the constraint that they are positive, and the answer turned out to be positive... so no problem with that)

    i dont get this part =S

    can u specify it further? =(
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