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Need help on another optimization problem!

  1. Mar 10, 2005 #1


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    Problem: An open top box is constructed from a sheet of material by cutting equal squares from each corner and folding up the edges. If the sheet of material measures 14 inches by 9 inches, find the dimension x which represents the length of one side of the square that should be cut off so that the volume is maximized.

    Work Done (Please Check!):

    Length: [tex]L(x)=-2x+14[/tex]

    Width: [tex]W(x)=-2x+9[/tex]

    Height: [tex]H(x)=x[/tex]

    Volume: [tex]V(x)=4x^{3}-46x^{2}+126x[/tex]

    This is where I am stuck:


    I need to factor out the derivative so that I can get the critical numbers. Unless I did something wrong, from what I got above it's not going to be whole numbers. I always have problems with fractions. :redface:
  2. jcsd
  3. Mar 10, 2005 #2

    this is more of a calc problem than physics

    get a ti89 :D

    i get the zeroes as 5.88 and 1.79...if you take the 2nd derivative you can find out which is the max and which is the min...
  4. Mar 10, 2005 #3


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    Thanks for your advice and solution.

    P.S. No offense, this forum deals with all subjects even though it is called Physics Forums. This is college homework so that is why I posted this here. If you look at other threads in this section, you will also find other calculus problems. And about the TI-89, I can't use calculators on tests.
    Last edited: Mar 10, 2005
  5. Mar 10, 2005 #4
    if she gives you problems like that she better!

    of course if she gives you a similar problem it will easily be factored

    basically you just find the zeroes of the derivative function...either with an 89 or using factoring
  6. Mar 10, 2005 #5


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    Yea, I think it's ridiculous that we can't use calculators on tests. Fortunately, this is only a practice problem. Hopefully they won't have something like this on the test. Thanks again!
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