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December 5th, 2009, 07:42 AM  #1 
Member Joined: Sep 2009 Posts: 69 Thanks: 0  hey can you help, word problem question
The management of a large store has 1600 feet of fencing to fence in a rectangular storage yard using the building as one side of the yard. If the fencing is used for the remaining 3 sides, find the area of the largest possible yard. i did x(16002x) the find derivative and solved for x and i got 800 times 400 = 320,000 is this correct? i wanted to see a picture of this problem, so i can better understand it 
December 5th, 2009, 07:58 AM  #2 
Senior Member Joined: Nov 2008 Posts: 265 Thanks: 0  Re: hey can you help, word problem question
well you have the perimeter x +2y = 1600 since one side of the fence will be parallel to the building and the other two parallel to each other. This equation will be your constraint and will allow you to get the Area in terms of one variable. So to find the largest possible area, you have the equation A=xy, but using the perimeter equation, you can get the Area in terms of one variable: x = 16002y. So A = (16002y)(y), A = 1600y  2y^2. Find the first derivative, find the critical pt. then find the second derivative to prove if the area will be a maximum, which will happen if the second derivative says the function will be concave down. After that, plug in the critical point, the y value, into the Perimeter equation and you get x. Then find the Area.

December 5th, 2009, 08:09 AM  #3 
Member Joined: Sep 2009 Posts: 69 Thanks: 0  Re: hey can you help, word problem question
so i got the answer(320,000), but i like to see a picture of it how i would i draw it 
December 5th, 2009, 08:37 AM  #4 
Senior Member Joined: Nov 2008 Posts: 265 Thanks: 0  Re: hey can you help, word problem question
Just draw a three sided fence and on the fourth side draw a building that is parallel to the opposite side

December 5th, 2009, 09:23 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,978 Thanks: 2229 
x(1600  2x) = 320000  2(x  400)² Alternatively, consider what happens if you have twice the length of fencing and don't use the building. 

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