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Math Help - Optimisation

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    Optimisation

    The sum of two numbers is 70. Find the numbers if their product is a maximum.

    Show steps please!
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by bubbles73 View Post
    The sum of two numbers is 70. Find the numbers if their product is a maximum.

    Show steps please!
    Let x and y be positive numbers.

    Thus, x+y=70

    However, their product P=xy must be a maximum.

    Since x+y=70\implies x=70-y

    Thus, we see that P=(70-y)y\implies P=70y-y^2

    Since it has to be a maximum, differentiate and set equal to zero.

    P'=70-2y\implies 70=2y\implies \color{red}\boxed{y=35}

    Now that we found y, we can find x:

    x+35=70\implies \color{red}\boxed{x=35}

    I hope this makes sense!

    --Chris
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