Results 1 to 2 of 2

Math Help - optimzation problem #5

  1. #1
    Senior Member
    Joined
    Nov 2008
    Posts
    425

    optimzation problem #5

    The cost of producing an ordinary cylindrical tin can is determined by the materials used for the wall and the end points. If the end pieces are twice as expensive per square cm as the wall, find the dimensions (to the nearest millimeter) to make a 1000 cm^3 can at minimal cost.

    Here is my work.. but does not lead to correct answer

    End pieces are 2k/cm
    Wall pieces are k/cm

    Min cost
    =2k(2pi(r^2))+k(2pi)(h)
    =2k(2pi)(r^2)+k(2pi(1000/(pi(r^2))
    =4pi(k)(r^2)+2000k(r^-2)
    C'(r)=8pi(k)(r)-4000k(r^-3)

    C'(r)=0 when r=aprox 1.99

    However, their answer is
    r=43 mm and height = 172 mm.
    Last edited by mr fantastic; August 12th 2009 at 04:44 PM. Reason: Changed post title
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,116
    Thanks
    1000
    Quote Originally Posted by skeske1234 View Post
    The cost of producing an ordinary cylindrical tin can is determined by the materials used for the wall and the end points. If the end pieces are twice as expensive per square cm as the wall, find the dimensions (to the nearest millimeter) to make a 1000 cm^3 can at minimal cost.

    Here is my work.. but does not lead to correct answer

    End pieces are 2k/cm
    Wall pieces are k/cm

    Min cost
    =2k(2pi(r^2))+k(2pi)r(h) ... forgot an r in the lateral surface area
    ...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. optimzation problem # 10
    Posted in the Calculus Forum
    Replies: 5
    Last Post: August 16th 2009, 11:12 PM
  2. optimzation problem # 10
    Posted in the Calculus Forum
    Replies: 7
    Last Post: August 13th 2009, 05:14 PM
  3. optimzation problem # 22
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 13th 2009, 11:55 AM
  4. optimzation problem #4
    Posted in the Calculus Forum
    Replies: 3
    Last Post: August 12th 2009, 05:20 PM
  5. optimzation problem #9
    Posted in the Calculus Forum
    Replies: 3
    Last Post: August 12th 2009, 08:37 AM

Search Tags


/mathhelpforum @mathhelpforum