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Math Help - Optimization problem (finding 2 numbers given an criteria)

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    Optimization problem (finding 2 numbers given an criteria)

    Find two numbers with a difference of 54 such that the square of one number multiplied by 6 times the other is a minimum.

    I'm not sure how I would go about making a relevant equation. x-y=54 seems simple enough, but I don't know what to do for the second.
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    x-y=54 \implies x=54+y

    Now

    x^2\times 6y = min

    (54+y)^2\times 6y = min

    Solve for

    ((54+y)^2\times 6y)' =0
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  3. #3
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    Quote Originally Posted by IanCarney View Post
    Find two numbers with a difference of 54 such that the square of one number multiplied by 6 times the other is a minimum.

    I'm not sure how I would go about making a relevant equation. x-y=54 seems simple enough, but I don't know what to do for the second.
    x - y = 54 \, \implies \, y = x-54

    P = x^2\cdot 6(x - 54)

    minimize the product, P
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