Question 872829
A field is bounded on one side by a river. A farmer wants to enclose the other three sides of the field with a fence in order to create a rectangular plot of land for his cows. If the farmer has 400m of fence to work with, determine the maximum possible area of the field and the field's dimensions. 
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Let x = width
and y = length
2x+y = 400 (eq 1)
xy= area   (eq 2)
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Solving eq 1 for y:
y = 400-2x
substitute into eq 2
x(400-2x) = area
-2x^2+400x = area
since the above is a parabola that opens downwards, the vertex is the max.
x-value of the max is:
x = -b/(2a)
x = -400/(2(-2))
x = -400/(-4)
x = 100 feet (width)
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length is:
2x+y=400
2(100)+y=400
200+y=400
y = 200 feet
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Max area is:100*200 = 20000 square feet