Question 995507: Good morning distinguished Tutors,i kindly need help with the following question-------"A mining company has 10 000 meters of fencing available .It wants to use the fencing to enclose a rectangular field .One side of the field is bordered by a river .If no fencing is placed on the side next to the river ,what is the largest area that can be enclosed?"
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! "A mining company has 10 000 meters of fencing available .It wants to use the fencing to enclose a rectangular field .One side of the field is bordered by a river .If no fencing is placed on the side next to the river ,what is the largest area that can be enclosed?"
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Sketch the picture
Let length of the rectangle = L
There are two widths; each is W
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L + 2W = 10,000 meters
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Area = L*W
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Substitute to get:
A = (10,000-2W)(W) = 10,000W - 2W^2
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Form the derivative and solve for zero
A' = 10,000-4W
10,000-4W = 0
4W = 10,000
W = 2500 (width to get maximum Area)
L = 10,000- 2(2500) = 5000 (length to get maximum Area)
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Cheers,
Stan H.
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