SOLUTION: 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

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.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
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.
***
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)
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