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Maximization problem

  1. Nov 19, 2006 #1
    OK, I've been killing myself over this one problem and I just cannot seem to get it. :grumpy: I know it's probably a lot easier than I'm making it out to be. If anyone can give me a little help I would really appreciate it. Here's the question:

    If 1200cm^2 of material is available to make a box with a square base and an open top, what is the box's larget possible volume?

    So far, I'm guessing that since the base of the box is to be square and there's an open top, the area of the box = x^2 + 4xy = 1200 and the volume = (x^2)y.

    I know at some point I'll need to differentiate and find the maximum of the function, but, I'm sort of floundering at this point. Thanks in advance.
     
  2. jcsd
  3. Nov 19, 2006 #2

    Hootenanny

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    Okay so you know have two functions, one of which you wish to maximise (i.e. the volume). Using your first equation can you write a function for y in terms of x?
     
  4. Nov 19, 2006 #3
    So, if I solve the first equation for y, I get y = (1200-x^2)/4x Is this correct?
     
  5. Nov 19, 2006 #4

    Hootenanny

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    Indeed it is. Can you guess what you need to do with this result? :wink:
     
  6. Nov 19, 2006 #5
    Plug that into my equation for volume, differentiate, and find the max?
     
  7. Nov 19, 2006 #6

    Hootenanny

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    Sounds good to me. :smile:
     
  8. Nov 19, 2006 #7
    Got it. That wasn't so hard, jeez. Thanks for the help! :)
     
  9. Nov 19, 2006 #8

    Hootenanny

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    No worries :smile:. Don't forget to verify that your answer is a maximum and is meaningful.
     
    Last edited: Nov 19, 2006
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