Question 193300: If I have the following: A farmer has 60 feet of fencing with which to enclose a rectangular pen adjacent to a long existing wall. He will use the wall for one side and the available fencing for the remaining three sides. If the sides perpendicular to the wall have length x feet, the area A of the enclosure is given by
A(x) = –2x2 + 60x.
I found the vertex which is :
The vertex is (15, 450)
A=-2
B=60
C=0
X=-b/2a
X= -60/[2*(-2)] = -60/-4 = 15
A(x) = -2(15)^2+60(15)
= -2(225)+900
= -450+900 = 450
Now, the following questions are:
Use the work in the previous parts to help determine the dimensions of the enclosure which yield the maximum area, and state the maximum area. (Fill in the blanks below. Include the units of measurement.)
The maximum area is:
when the sides perpendicular to the wall have length x =
and the side parallel to the wall has length x=
I know that A = 2L+2W but I am not sure how to determine those three... I thought the vertex would help me somehow but I got really confused...
Could you help me with this?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A farmer has 60 feet of fencing with which to enclose a rectangular pen adjacent to a long existing wall. He will use the wall for one side and the available fencing for the remaining three sides. If the sides perpendicular to the wall have length x feet, the area A of the enclosure is given by
A(x) = –2x2 + 60x = x(-2x+60).
I found the vertex which is :
The vertex is (15, 450)
A=-2
B=60
C=0
X=-b/2a
X= -60/[2*(-2)] = -60/-4 = 15
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This tells you the length of the side is 15 feet.
---
A(x) = -2(15)^2+60(15)
= -2(225)+900
= -450+900 = 450
---
This tells you the maximum area is 450 sq. ft.
---
Now, the following questions are:
Use the work in the previous parts to help determine the dimensions of the enclosure which yield the maximum area, and state the maximum area. (Fill in the blanks below. Include the units of measurement.)
The maximum area is: 450 sq. ft.
when the sides perpendicular to the wall have length x = 15 ft
and the side parallel to the wall has length x= -2x+60 = 30 ft
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Could you help me with this?
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Cheers,
Stan H.
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