Results 1 to 3 of 3

Math Help - Optimization (word problem)

  1. #1
    Newbie
    Joined
    Oct 2008
    Posts
    3

    Optimization (word problem)

    Ok, so the problem is about Optimization and I'm not really sure how to approach it.

    Minimum Cost An industrial tank (two hemispheres and a circular cylinder) must have a volume of 3000 cubic feet. The hemispherical ends cost twice as much per square foot of surface area as the sides. Find the dimensions that will minimize cost.

    Sadly I have only gotten the volume formula

    4/3π r^3+π r^2h=3000

    Any help would be appreciated. I'm not looking for a solution, but rather for a process. Thanks in advance.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    We must minimize the cost of the material, so we need the surface area.

    The surface area of the sphere is 4{\pi}r^{2}

    The surface area of the cylindrical portion is 2{\pi}rh

    S=4{\pi}r^{2}+2{\pi}rh

    Use the volume formula to solve for a variable and sub into the surface area formula so that it is in terms of one variable.

    Then, you can optimize. Don't forget to take into account the cost conditions given.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2008
    Posts
    3
    ah ok!

    I feel so stupid I didn't realize it was a surface area question
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. solving optimization word problem?
    Posted in the Calculus Forum
    Replies: 5
    Last Post: February 3rd 2011, 04:51 AM
  2. Optimization Word Problem Start Help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 17th 2009, 05:52 PM
  3. optimization word problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 1st 2008, 05:09 PM
  4. Practical Optimization Word Problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 16th 2007, 04:18 AM
  5. Grr (optimization word problem)
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 22nd 2006, 02:57 AM

Search Tags


/mathhelpforum @mathhelpforum