Results 1 to 6 of 6

Math Help - maximize

  1. #1
    Member
    Joined
    Mar 2008
    Posts
    88

    Exclamation maximize

    I can't even explain how lost i am on this problem so here it is.

    An indoor physical fitness room consists of a rectangular region with a semicircle on each end. If the perimeter of the room is to be a 200-meter running track, find the dimensions that will make the are of the rectangular region as large as possible.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by uniquereason81 View Post
    I can't even explain how lost i am on this problem so here it is.

    An indoor physical fitness room consists of a rectangular region with a semicircle on each end. If the perimeter of the room is to be a 200-meter running track, find the dimensions that will make the are of the rectangular region as large as possible.
    P=2\pi{r}+2x

    Solve for x and sub into your A equation

    Edit^(didnt read it again)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Apr 2008
    Posts
    1,092
    Quote Originally Posted by uniquereason81 View Post
    I can't even explain how lost i am on this problem so here it is.

    An indoor physical fitness room consists of a rectangular region with a semicircle on each end. If the perimeter of the room is to be a 200-meter running track, find the dimensions that will make the are of the rectangular region as large as possible.
    You want to maximize the area of a rectangular region, represented by xy, with the constraint of a 200 meter perimeter. The perimeter is going to be equal to the circumference of a circle (with diameter x) plus two sides (of length y) of the rectangle:
    \pi{x}+2y

    So given that \pi{x}+2y=200 maximize xy. Then I would assume you would use Lagrange multipliers.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by icemanfan View Post
    You want to maximize the area of a rectangular region, represented by xy, with the constraint of a 200 meter perimeter. The perimeter is going to be equal to the circumference of a circle (with diameter x) plus two sides (of length y) of the rectangle:
    \pi{x}+2y

    So given that \pi{x}+2y=200 maximize xy. Then I would assume you would use Lagrange multipliers.
    .......Lagrange multipliers? Why would you ever do that..solve the P equation in terms of the other variable...substitute it into your A equation...differentiate and proceed to find max by normal methods
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Apr 2008
    Posts
    1,092
    Quote Originally Posted by Mathstud28 View Post
    .......Lagrange multipliers? Why would you ever do that..solve the P equation in terms of the other variable...substitute it into your A equation...differentiate and proceed to find max by normal methods
    You're right, this problem isn't too complicated to require doing it that way.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by icemanfan View Post
    You're right, this problem isn't too complicated to require doing it that way.
    Haha you just tried to apply a Calc 3 method to a Calc 1 problem
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Maximize Profit
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 20th 2009, 11:04 PM
  2. maximize
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: November 14th 2008, 02:54 PM
  3. Please Help maximize!!
    Posted in the Algebra Forum
    Replies: 1
    Last Post: November 14th 2007, 07:27 PM
  4. Maximize
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 25th 2007, 06:08 AM
  5. please help minimize maximize
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 28th 2006, 11:30 AM

Search Tags


/mathhelpforum @mathhelpforum