January 23rd, 2010, 05:44 PM  #1 
Newbie Joined: Jan 2010 Posts: 8 Thanks: 0  Perimeter
A farmer has 4000m of fencing to enclose a rectangular field and subdivide it into three equal plots of land. Determine the dimensions of each plot of land so that the total area enclosed is a maximum. Pissing the **** out of me, me and 3other friends have been trying to solve this for the last 2hours. 
January 23rd, 2010, 06:21 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,923 Thanks: 1122 Math Focus: Elementary mathematics and beyond  Re: Perimeter
4x + 2y = 4000 2x + y = 2000 y = 2000  2x area = xy, so area = 2000x  2x^2, complete the square to find the xcoordinate of vertex (maximum point) of the area function, (x  500)^2  250000, so x = 500, y = 1000. 
January 23rd, 2010, 08:04 PM  #3 
Newbie Joined: Jan 2010 Posts: 8 Thanks: 0  Re: Perimeter
ok you get 2000x2x^2 Then you complete the square =2(x^21000x) =2(x^21000x+250000250000) =2(x500)+500000 Thats what I'm getting. Is there something I'm doing wrong? Also why is it 4x+2y=4000? 
January 23rd, 2010, 08:25 PM  #4  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,923 Thanks: 1122 Math Focus: Elementary mathematics and beyond  Re: Perimeter Quote:
Quote:
 
January 23rd, 2010, 08:38 PM  #5  
Newbie Joined: Jan 2010 Posts: 8 Thanks: 0  Re: Perimeter Quote:
My diagram is 3rectangles side by side because his field is subdivided into 3 smaller ones. I dont get where you got 4 x's and 2 y's.  
January 23rd, 2010, 08:42 PM  #6 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,923 Thanks: 1122 Math Focus: Elementary mathematics and beyond  Re: Perimeter
Sorry. I'm just trying to explain why the maximum area is when x is 500.

January 23rd, 2010, 09:15 PM  #7 
Newbie Joined: Jan 2010 Posts: 8 Thanks: 0  Re: Perimeter
ok

January 23rd, 2010, 10:03 PM  #8  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,923 Thanks: 1122 Math Focus: Elementary mathematics and beyond  Re: Perimeter Quote:
 
January 24th, 2010, 02:14 AM  #9 
Global Moderator Joined: Dec 2006 Posts: 20,370 Thanks: 2007 
Do the subplots need to be equal in size or just equal in area?

January 24th, 2010, 05:52 AM  #10 
Newbie Joined: Jan 2010 Posts: 8 Thanks: 0  Re: Perimeter
I think in area.


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