Results 1 to 2 of 2

Math Help - Optimization problem

  1. #1
    Newbie
    Joined
    Nov 2010
    Posts
    1

    Optimization problem

    a Donor is willing to build a new hangar for the program with the following stipulations
    - the hangar must be in the shape of a half cylinder
    - the hangar to have an exact volume of 225000 cubit feet
    We would like to minimize the cost of the building. Currently, the construction costs for the foundation are $30 per square foot, the sides cost $20 per square foot to construct, and the roofing costs $15 per square foot. what should the dimensions of the building be to minimize the total cost ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,872
    Thanks
    656
    Quote Originally Posted by genie2010 View Post
    a Donor is willing to build a new hangar for the program with the following stipulations
    - the hangar must be in the shape of a half cylinder
    - the hangar to have an exact volume of 225000 cubit feet
    We would like to minimize the cost of the building. Currently, the construction costs for the foundation are $30 per square foot, the sides cost $20 per square foot to construct, and the roofing costs $15 per square foot. what should the dimensions of the building be to minimize the total cost ?
    - the hangar must be in the shape of a half cylinder ... V = \frac{\pi}{2}r^2 h

    - the hangar to have an exact volume of 225000 cubic feet ... 225000 = \frac{\pi}{2}r^2 h

    foundation area ... F = 2rh

    roof area ... R = \pi r h

    "sides" (actually, the vertical ends) area = \pi r^2

    set up a cost function, get the cost function in terms of a single variable ( r or h, whichever is easier), and find the value of that variable that minimizes the cost using the techniques taught to you in class.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Optimization Problem
    Posted in the Calculus Forum
    Replies: 6
    Last Post: August 3rd 2010, 10:37 AM
  2. Optimization Problem
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: March 27th 2010, 01:35 PM
  3. optimization problem
    Posted in the Advanced Applied Math Forum
    Replies: 0
    Last Post: January 24th 2010, 12:17 PM
  4. optimization problem.
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 22nd 2009, 06:04 PM
  5. optimization problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 25th 2007, 10:20 PM

Search Tags


/mathhelpforum @mathhelpforum