Results 1 to 5 of 5

Math Help - Maximization Problem

  1. #1
    Member
    Joined
    Mar 2008
    Posts
    95

    Maximization Problem

    Just wondering the basic process into solving this one.

    A square is to be cut from each corner of a piece of paper which is 8cm by 10cm, and the sides are to be folded up to create an open box. What should the side of the square be for maximum volume?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Mar 2008
    Posts
    95
    Nvm I solved it
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by Hibijibi View Post
    Just wondering the basic process into solving this one.

    A square is to be cut from each corner of a piece of paper which is 8cm by 10cm, and the sides are to be folded up to create an open box. What should the side of the square be for maximum volume?
    Maximization Problem-capture.jpg

    so the volume of the box will be

    V=l\cdot w \cdot h =(10-2x)(8-2x)x=80x-36x^2+4x^3

    taking the derivative we get the max and min points

    answer is below (if you scroll down.)






















    \frac{dV}{dx}=80-72x+12x^2

    using the quadratic formula we get

    x=\frac{-(-72) \pm \sqrt{(-72)^2}-4(12)(80)}{2(12)}=3 \pm \frac{\sqrt{21}}{3}
    Last edited by TheEmptySet; May 10th 2008 at 09:25 PM. Reason: lost a few 2's. :(
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Mar 2008
    Posts
    95
    Forgot about quadratic, I just graphed and found 0s that way. Also you forgot to use (10-2x)(8-2x)(x), instead of (10-x)(8-x)(x). You get different answers if you forget the 2x.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by Hibijibi View Post
    Forgot about quadratic, I just graphed and found 0s that way. Also you forgot to use (10-2x)(8-2x)(x), instead of (10-x)(8-x)(x). You get different answers if you forget the 2x.
    Yep. They are in my diagram but not my equations, I will fix it.

    Thanks
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Maximization Problem
    Posted in the Pre-Calculus Forum
    Replies: 8
    Last Post: May 21st 2011, 05:36 PM
  2. maximization problem
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: March 14th 2011, 11:59 AM
  3. [SOLVED] maximization problem
    Posted in the Business Math Forum
    Replies: 2
    Last Post: July 23rd 2010, 05:34 PM
  4. maximization problem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 5th 2009, 07:23 PM
  5. Maximization Problem Help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 17th 2008, 07:10 PM

Search Tags


/mathhelpforum @mathhelpforum