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Homework Help: Optimization finding expression

  1. Mar 26, 2006 #1
    http://img117.imageshack.us/img117/3055/diagram28do.jpg [Broken]

    I drew out that diagram but I think I might be wrong. The question is:

    Tom makes an open box from a rectangular piece of metal by cutting equal squares from the four corners and turning up the sides. The piece of metal measures 60 x 100 cm. What are the dimensions of the box with the maximum volume?
     
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Mar 26, 2006 #2
    I wrote A=(60-2x)(100-2y)
     
  4. Mar 26, 2006 #3
    [tex]V = l.w.h[/tex]
    [tex]V = (100-2y)(60-2x)(y)[/tex]

    If he cut squares from the four corners, then y = x.

    [tex]V = (100-2x)(60-2x)(x)[/tex]

    Find the maximum value of V for positive values of x and you have your solution.
     
  5. Mar 26, 2006 #4
    OHH...Right. Okay, thank you!
     
  6. Mar 26, 2006 #5
    Okay this is strange...
    After expanding and simplifying, I get
    V=4x^3-320x^2+6000x

    I differentiate that too
    V'=12x^2-640x+6000

    but I'm not getting the answer in the textbook. What am I doing wrong?
     
  7. Mar 26, 2006 #6
    nvm...I should have differentiated using the product rule D8
     
  8. Mar 26, 2006 #7
    no...didn't make a different and Im still getting a weird answer. Can someone please help me?
     
  9. Mar 26, 2006 #8
    Ignore last post! D8
     
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