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 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: 7,935 Thanks: 1129 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 x-coordinate 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 2000x-2x^2 Then you complete the square =-2(x^2-1000x) =-2(x^2-1000x+250000-250000) =-2(x-500)+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
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Re: Perimeter

Quote:
 Originally Posted by ExIsTaNcE ok you get 2000x-2x^2 Then you complete the square =-2(x^2-1000x) =-2(x^2-1000x+250000-250000) =-2(x-500)+500000 Thats what I'm getting. Is there something I'm doing wrong?
Nope. It should be -2(x - 500)^2 + 500000, but I think you just left out the "^2" part. Anyway, look at -2(x - 500)^2 + 500000. You're subtracting 2(x - 500)^2 from 500000. 2(x - 500)^2 is either zero or positive, therefore the function is at it's maximum when this is equal to zero, that is, when x = 500.

Quote:
 Originally Posted by ExIsTaNcE Also why is it 4x+2y=4000?
Make a diagram of what the three plots may look like.

January 23rd, 2010, 08:38 PM   #5
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Re: Perimeter

Quote:
 Originally Posted by greg1313 Anyway, look at -2(x - 500)^2 + 500000. You're subtracting 2(x - 500)^2 from 500000. 2(x - 500)^2 is either zero or positive, therefore the function is at it's maximum when this is equal to zero, that is, when x = 500.
We're subtracting? I'm lost in this explanation. Our teacher never taught us anything about subtracting, or a question relating to this

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: 7,935 Thanks: 1129 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
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Re: Perimeter

Quote:
 Originally Posted by ExIsTaNcE 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.
You need 4 pieces of length x and 2 pieces of length y to divide the field into 3 equal plots.

 January 24th, 2010, 02:14 AM #9 Global Moderator   Joined: Dec 2006 Posts: 20,627 Thanks: 2077 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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