Question 892746
A farmer is fencing a rectangular area for his farm using the straight portion of a river as one portion of the rectangle. If the farmer has 2400 feet of fence, find the dimension of the rectangle that gives the maximum area for the farm.
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let x=width (2 sides)
2400-2x=length(1 side)
area=length*width=x(2400-2x)=2400x-2x^2
f(a)=-2x^2+2400
complete the square:
f(a)=-2(x^2-1200+360000)+720000
f(a)=-2(x-600)^2+720000
This is an equation of a parabola that opens down with vertex at (600,720,000)
dimension of the rectangle that gives the maximum area of 720,000 sq ft for the farm:
width=600 ft (2 sides)
length=1200 ft (single side)