Results 1 to 3 of 3

Math Help - optimization

  1. #1
    Newbie
    Joined
    Apr 2009
    Posts
    3

    Question optimization

    A cylindrical can, open at the top, is to hold 1000cm^3 of liquid. The material for the side of the can costs $.50 per cm^2 to manufacture, and the material for the base costs $.75 per cm^2 to manufacture. Find the height and radius that minimize the cost to manufacture the can.

    Does anyone know how to solve this problem? I'm a bit lost.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,623
    Thanks
    428
    Quote Originally Posted by bluebyte22 View Post
    A cylindrical can, open at the top, is to hold 1000cm^3 of liquid. The material for the side of the can costs $.50 per cm^2 to manufacture, and the material for the base costs $.75 per cm^2 to manufacture. Find the height and radius that minimize the cost to manufacture the can.

    Does anyone know how to solve this problem? I'm a bit lost.
    volume information ...

    \pi r^2 h = 1000

    h = \frac{1000}{\pi r^2}

    surface area ...

    A = \pi r^2 + 2\pi rh

    A = \pi r^2 + 2\pi r \left(\frac{1000}{\pi r^2}\right)

    cost ...

    C = .75(\pi r^2) + .50\left[2\pi r \left(\frac{1000}{\pi r^2}\right)\right]

    clean up the algebra for the cost function, find \frac{dC}{dr} and minimize the cost.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2009
    Posts
    3

    Red face

    Thank you
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. optimization help!
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 12th 2009, 12:54 AM
  2. Optimization
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 8th 2009, 02:09 PM
  3. Optimization
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 29th 2009, 10:56 AM
  4. optimization
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 12th 2008, 10:47 AM
  5. Optimization
    Posted in the Pre-Calculus Forum
    Replies: 0
    Last Post: October 13th 2008, 06:44 PM

Search Tags


/mathhelpforum @mathhelpforum