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Math Help - Modelling help!!!

  1. #1
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    Exclamation Modelling help!!!

    Hi,
    Currently doing a problem with max/min problems and Maximizing the volume.
    A sheet of cardboard 30cm by 40cm is to be cut into a box with a lid. The box shape is one of a rectangular cereal box.

    I have worked the total area to be:
    120cm^2 = 2zy + 2xy + 2xz

    But im now stuck on what to do?

    I need to find the dimensions that will maximise the volume and prove that its a maximum.
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  2. #2
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    Does the lid have to be made out of the same sheet of cardboard?

    If not then you might be able to say that the Volume is x(30-2x)(40-2x) if you cut the corners of the sheet out as a square and make the box by folding up the edges.
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  3. #3
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    thanks for a reply.
    yes there does need to be a lid on it.
    The equation i gave earlier im not to sure if its right.
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  4. #4
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    Quote Originally Posted by kiwimate View Post
    The equation i gave earlier im not to sure if its right.
    Neither am I, is there any other information? Does the lid need to be cut from that sheet of cardboard?
    Last edited by pickslides; January 19th 2011 at 04:32 PM. Reason: *sp
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  5. #5
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    The question is:
    A sheet of cardboard 30cm by 40cm is to be cut into a box with a lid, as shown below.
    Find the dimensions of the box that maximise the volume it contains.
    Hint: remember to show that it is indeed a maximum.

    The net is the same as this shape, however x,y,z are all different lengths.
    http://spmath84109.blogspot.com/2010_02_01_archive.html
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  6. #6
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    Sorry, the server here is not finding that link.
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  7. #7
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    damm link..
    its basically a net that would make up a cube except x,y,z all different lengths
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  8. #8
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    Quote Originally Posted by kiwimate View Post
    Hi,
    Currently doing a problem with max/min problems and Maximizing the volume.
    A sheet of cardboard 30cm by 40cm is to be cut into a box with a lid. The box shape is one of a rectangular cereal box.
    make a sketch ...

    V = x(30-2x)(20-x)
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