SOLUTION: Suppose a farmer has 500 feet of fence and wants to enclose part of his existing pasture to make a special pen for animals. Since there is already some fencing he only needs to add

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Question 1131205: Suppose a farmer has 500 feet of fence and wants to enclose part of his existing pasture to make a special pen for animals. Since there is already some fencing he only needs to add fencing on three sides. The area functions would be A(x)=-2x^2+500x where A is the area of the pen and x is the width of the pen. Find the maximum area he can enclose.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Suppose a farmer has 500 feet of fence and wants to enclose part of his existing pasture to make a special pen for animals.
Since there is already some fencing he only needs to add fencing on three sides.
The area functions would be A(x)=-2x^2+500x where A is the area of the pen and x is the width of the pen.
Find the maximum area he can enclose.
:
The is a quadratic equation, therefore the max area occurs on the axis of symmetry.
Use the formula x = -b/(2a), where a=-2; b=500
x = %28-500%29%2F%282%2A-2%29
x = 125 ft is the width for max area
:
" Find the maximum area he can enclose."
x = 125
A+=+-2%28125%5E2%29%2B500%28125%29
A = -31250 + 62500
A = 31,250 sq/ft