Results 1 to 2 of 2

Math Help - Optimization question

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    5

    Optimization question

    A soup can of volume 500cm^3 is to be constructed.
    The material for the top costs 0.4cents/cm^2 wwhile the material for the bottom and sides costs 0.2cents/cm^2. Find the dimensions that will minimize the cost of producing the can.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Oct 2009
    Posts
    32
    Quote Originally Posted by bebejay View Post
    A soup can of volume 500cm^3 is to be constructed.
    The material for the top costs 0.4cents/cm^2 wwhile the material for the bottom and sides costs 0.2cents/cm^2. Find the dimensions that will minimize the cost of producing the can.
    You have two equations to consider:
    V = πr^2h,
    SA = 2πrh(side) + πr^2 (top) + πr^2(bottom)
    thus: 500 = πr^2h, h = 500/(πr^2)

    SA = 2πr(500/(πr^2) + πr^2 + πr^2
    SA(including cost) = 0.4[2πr(500/(πr^2)] + 0.4[πr^2] + 0.2[πr^2]
    I think now you find the derivative which should tell you what r is, and then plug in to find the dimensions.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Optimization Question
    Posted in the Calculus Forum
    Replies: 6
    Last Post: May 3rd 2010, 05:11 AM
  2. Question on Optimization
    Posted in the Calculus Forum
    Replies: 0
    Last Post: December 8th 2009, 12:03 AM
  3. Optimization question
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 16th 2009, 10:18 PM
  4. another optimization question
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 29th 2009, 08:41 PM
  5. Optimization question 1
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 23rd 2009, 07:09 PM

Search Tags


/mathhelpforum @mathhelpforum