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December 5th, 2009, 07:42 AM   #1
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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(1600-2x) 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
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December 5th, 2009, 07:58 AM   #2
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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 = 1600-2y. So A = (1600-2y)(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.
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December 5th, 2009, 08:09 AM   #3
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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
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December 5th, 2009, 08:37 AM   #4
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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
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December 5th, 2009, 09:23 PM   #5
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x(1600 - 2x) = 320000 - 2(x - 400)

Alternatively, consider what happens if you have twice the length of fencing and don't use the building.
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