Results 1 to 6 of 6
Like Tree1Thanks
  • 1 Post By ione

Math Help - Optimization word problem

  1. #1
    Member
    Joined
    Jun 2012
    From
    Australia
    Posts
    86

    Optimization word problem

    I have a question that is as follows..

    Homing pigeons avoid flying over large bodies of water, preferring to fly around them instead (One possible explanation is the fact that extra energy is required to fly over water). Assume a pigeon is released from a boat 1 mile from the shore of a lake (Point B), flies first to point P on the short and then along the straight edge of the lake to reach its home at L. If L is 2 miles from point A, the point on the shore closest to the boat, and if a pigeon needs 4/3 as much energy per mile to fly over water as over land, find the location of point P, which minimizes energy used.

    So Obviously I need to find the absolute minimum, and to do this, I need to create a function, differentiate it, find the critical number and then plug that into the formula to find the extrema.

    I don't know if I'm setting the function up correctly though, and I'm also having a bit of trouble differentiating the function I do have set up.

    http://i1162.photobucket.com/albums/...Misc/photo.jpg

    That's an image of my working, though I don't think its correct, because the final value I Get can not be correct..
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Feb 2010
    Posts
    148
    Thanks
    2

    Re: Optimization word problem

    E'(x)=\frac{4x}{3\sqrt{x^2+1}}-1
    Last edited by ione; September 25th 2012 at 07:13 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jun 2012
    From
    Australia
    Posts
    86

    Re: Optimization word problem

    Quote Originally Posted by ione View Post
    E'(x)=\frac{4x}{3\sqrt{x^2+1}}-1
    Whoops, that's a silly mistake.

    Ok, so to find the critical number is as follows....

    e '(x) = (4x / 3[x^2 + 1]^{1/2}) - 1

    = 4x / 3(x^2 + 1)^{1/2} = 1

    = 4x = 3(x^2+1)^{1/2}

    =(4x/3) = (x^2 + 1)^{1/2}

    (16x^2 / 9) = x^2 - 1

    =16x^2 = 9x^2 - 9

    = 7x^2 = 9

    = x^2 = (9/7)

    = x = (3 / (7)^{1/2})

    This seems to get an answer that is more in line with what the question is asking, but when I corrected my work in the back of the book, the critical number it came up with was this...

    3(7)^{1/2} / 7

    I can't see where I've gone wrong in the solving of the critical number though...
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Feb 2010
    Posts
    148
    Thanks
    2

    Re: Optimization word problem

    \frac{3}{\sqrt{7}}=\frac{3\sqrt{7}}{7}
    Thanks from astuart
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Sep 2012
    From
    Washington DC USA
    Posts
    525
    Thanks
    146

    Re: Optimization word problem

    Quote Originally Posted by astuart View Post
    ...

    =(4x/3) = (x^2 + 1)^{1/2}

    (16x^2 / 9) = x^2 - 1

    ...
    See it?

    Nevermind, you switched it back later (the -9 became a plus +9 for no reason). This is one of those "two wrongs do make a right" situations.
    Last edited by johnsomeone; September 25th 2012 at 09:27 PM.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Jun 2012
    From
    Australia
    Posts
    86

    Re: Optimization word problem

    Quote Originally Posted by johnsomeone View Post
    See it?

    Nevermind, you switched it back later (the -9 became a plus +9 for no reason). This is one of those "two wrongs do make a right" situations.
    Whoops, didn't notice that either...Need to check my working better.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Optimization Word Problem Start Help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 17th 2009, 05:52 PM
  2. Optimization (word problem)
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 10th 2009, 10:05 AM
  3. optimization word problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 1st 2008, 05:09 PM
  4. Practical Optimization Word Problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 16th 2007, 04:18 AM
  5. Grr (optimization word problem)
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 22nd 2006, 02:57 AM

Search Tags


/mathhelpforum @mathhelpforum