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Math Help - Calc 1: Urgent, Optimize

  1. #1
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    Calc 1: Urgent, Optimize

    A shipping company limits the size of a mailable parcel. The longest side plus the girth (the perimeter of a cross section perpendicular to the longest side) may not exceed 108 inches" 1.) Which mailable cube has the largest volume? 2.) Find the dimensions of the mailable rectangular parcel with a square base that has the largest volume. 3.) Among mailable right circular cylinders, which has the largest volume?

    This is due in 10-15 mins if someone by chance reads this in time. Thanks
    Last edited by CaptainBlack; December 6th 2006 at 09:18 PM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Bloden View Post
    A shipping company limits the size of a mailable parcel. The longest side plus the girth (the perimeter of a cross section perpendicular to the longest side) may not exceed 108 inches" 1.) Which mailable cube has the largest volume? 2.) Find the dimensions of the mailable rectangular parcel with a square base that has the largest volume. 3.) Among mailable right circular cylinders, which has the largest volume?

    This is due in 10-15 mins if someone by chance reads this in time. Thanks

    1) For a cube the girth plus the longest side is 5s, where s is the length of the side.
    So for the largest cube:

    5s=108,

    or

    s=21.6 inches

    2) Let the side of the square base be s and the length be l, then:

    4s+l=108,

    The volume is:

    V=s^2 x l=s^2 (108-4s)

    The largest volume corresponds to one of the solutions of dV/ds=0, so:

    216 s -12s^2=0,

    one root is s=0, which is not the one we want, the other is s=216/12=18 inches,
    from which we get l=36 inches.

    3) solution method is similar to 2)

    RonL
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