Results 1 to 5 of 5

Math Help - word problem, Maximum

  1. #1
    Super Member
    Joined
    Sep 2008
    Posts
    607

    word problem, Maximum

    You have a given length of fence. Using the wall of a house as one side of a rectangular fence, how would you place the fence around the other three sides in order to enclose the largest possible area?
    Not sure how to begin, any help appreciated.

    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Mar 2008
    Posts
    182
    Quote Originally Posted by Tweety View Post
    Not sure how to begin, any help appreciated.

    Thanks!
    The question says that the fence is rectangular... and you have the wall of the house as one side...

    So surely you have the dimensions there...?

    The more interesting question would surely be if the house were not rectangular - how would you maximise the area it covered (but still using the wall of the house as one side...)?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Sep 2008
    Posts
    607
    Quote Originally Posted by Unenlightened View Post
    The question says that the fence is rectangular... and you have the wall of the house as one side...

    So surely you have the dimensions there...?

    The more interesting question would surely be if the house were not rectangular - how would you maximise the area it covered (but still using the wall of the house as one side...)?
    A=xy ?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Like a stone-audioslave ADARSH's Avatar
    Joined
    Aug 2008
    From
    India
    Posts
    726
    Thanks
    2
    The question would "most probably" state that house is taken as one of the edges of fence
    Lets say that the length of fence = P = Perimeter = 2(L + B)

    You need to find the macximum value of A= L*B = (P/2 -B) B

    You need to find value of B for which A is maximum.


    ie;

    \frac{d\frac{P/2 - B}{B}}{dB} = 0

    treat P/2 as a constant while you differentiate

    Find B from above thing and that will lead you to L as well
    thus we would know length and breadth.

    Now come forward and show the steps
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,662
    Thanks
    603
    Hello, Tweety!

    You have a given length of fence.
    Using the wall of a house as one side of a rectangular fence, how would you place
    the fence around the other three sides in order to enclose the largest possible area?
    Code:
        ~ * ~ ~ ~ ~ ~ * ~
          |           |
        x |           | x
          |           |
          * - - - - - *
                y

    The amount of fencing is a constant, k feet.

    . . So we have: . 2x + y \:=\:k \quad\Rightarrow\quad y \:=\:k-2x .[1]


    The area of the region is: . A \:=\:xy .[2]

    Substitute [1] into [2]: . A \:=\:x(k-2x) \quad\Rightarrow\quad A \;=\;kx-2x^2


    This is a parabola that opens downward.
    . . Its maximum is at its vertex.
    The vertex is at: . \frac{\text{-}b}{2a}
    . . So we have: . x \:=\:\frac{\text{-}k}{2(\text{-}2)} \:=\:\frac{k}{4}


    We will use \frac{k}{4} feet (a quarter of the fencing) for each of the two shorter sides
    . . and the rest, \frac{k}{2} feet, for the long side.

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. maximum value problem
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 22nd 2011, 10:55 AM
  2. maximum value problem
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: September 21st 2011, 11:43 AM
  3. Minimum/Maximum Word Problem
    Posted in the Calculus Forum
    Replies: 0
    Last Post: September 6th 2011, 12:07 PM
  4. Maximum Problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 27th 2009, 04:51 PM
  5. Maximum problem
    Posted in the Calculus Forum
    Replies: 7
    Last Post: July 13th 2009, 02:01 PM

Search Tags


/mathhelpforum @mathhelpforum