divide 50 into two parts such that the product will be a maximum

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  1. one part --- x
    the other part ---- 50-x

    product = y = x(50-x)
    y = -x^2 + 50x

    this is a downwards opening parabola, so it has a maximum
    Use your favourite method to find that vertex and the mystery
    will be revealed to you.

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  2. ????

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