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Math Help - Applied Optimization Problem

  1. #1
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    Applied Optimization Problem

    Hey guys I've been trying this problem for an hour now and I am stuck:

    Among all positive numbers a, b whose sum is 8, find those for which the product of the two numbers and their difference is largest.



    answers are = 4 + and - ((4rad3)/3)
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  2. #2
    Member Mentia's Avatar
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    i dont fully understand what you mean by "the product of the two numbers and their difference is largest."

    do you want the biggest product or the biggest difference? which one?

    biggest difference is obvious: 8 and 0

    they have to be positive numbers:

    a + b = 8 ---> b = (8 - a)

    let z = ab, then z = a*(8-a). dz/da = -2a + 8. there are extrema when dz/da = 0. so set:

    0 = -2a + 8 ----> a = 4 -----> b = 4

    thus a = 4 and b = 4
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  3. #3
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    nvm got it =P
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