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Math Help - Optimizing Equations

  1. #1
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    Optimizing Equations

    Hi everyone.
    Boy do I have a fun one for you today!

    A peice of sheet metal has 4800 cm^2 area.
    Create an open top box with a quare bottom that has the largest
    possible volume. Did not get very far on this one. I have no idea how
    to solve this problem. :P
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  2. #2
    Moo
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    Hello,

    Quote Originally Posted by ffezz View Post
    Hi everyone.
    Boy do I have a fun one for you today!

    A peice of sheet metal has 4800 cm^2 area.
    Create an open top box with a quare bottom that has the largest
    possible volume. Did not get very far on this one. I have no idea how
    to solve this problem. :P
    Is there an information about the shape of the box, or the dimensions of the square bottom ?
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  3. #3
    Super Member flyingsquirrel's Avatar
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    Hi
    Quote Originally Posted by Moo View Post
    Is there an information about the shape of the box, or the dimensions of the square bottom ?
    If it were the case, I think the problem couldn't be solved, there would be too many conditions. (unless it is useless information )

    Lets call h the height of the box and x its width.
    Quote Originally Posted by ffezz View Post
    A peice of sheet metal has 4800 cm^2 area.
    This gives a relation between x and h (the area of the box is the sum of the area of each side and has to be 4800\mathrm{cm}^2)

    Then, you should know what is the volume of the box in function of x and h and, thanks to what you've done before, you can rewrite it as a function of only one variable. (say h)

    that has the largest possible volume.
    This gives a condition on the derivative of the volume which gives us h and from which we get x.
    Last edited by flyingsquirrel; April 29th 2008 at 12:09 PM.
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