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Math Help - Optimization largest volume

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    Optimization largest volume

    Postal regulations specify that a parcel sent by parcel post may have a combined length and girth of no more than 120 in. Find the dimensions of a rectangular package that has a square cross section and the largest volume that may be sent through the mail.
    (Hint: The length plus the girth is 4x+h )
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by tim22 View Post
    Postal regulations specify that a parcel sent by parcel post may have a combined length and girth of no more than 120 in. Find the dimensions of a rectangular package that has a square cross section and the largest volume that may be sent through the mail.
    (Hint: The length plus the girth is 4x+h )
    Here the side length of the end is x, and the length is h.

    Thus, the volume is given by: V = x^2h

    now our constraint is that the length plus girth must be less than or equal to 120. thus we must have that

    4x + h \le 120

    now solve for h, we get:

    h \le 120 - 4x

    we have the largest volume when h is as large as possible, thus take h to be such that h = 120 - 4x

    thus, plugging this into our volume equation, we get:

    V = x^2 (120 - 4x)

    \Rightarrow V = 120x^2 - 4x^3

    now this last function is what we want to maximize. can you continue?
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    yes i figured it out, thank you very much
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by tim22 View Post
    yes i figured it out, thank you very much
    you're welcome
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