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    Important information about Maximization

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    Find two real numbers whose sum is 10 and whose product is maximal?

    © BrainMass Inc. brainmass.com February 24, 2021, 2:08 pm ad1c9bdddf

    Solution Preview

    Let x and (10-x) be the two numbers. We must find x such that the product,

    P(x) = x(10-x) (1)

    is maximal. Expanding this equation we have

    P(x) = 10x-x^2 (2)

    As the reader can see, this is just a parabola opening downward, (I call this a frowning parabola ...

    Solution Summary

    This shows how to find two numbers with maximum product and given sum.