Pen Fence

Pen Fence
A home owner has 80 ft of fencing to be used to construct a dog pen adjacent to a house…?

(so only 3 sides will be fenced). Express the are A(x) enclosed by the pen as a function of the width, x. Then find the dimensions of the pen that will maximize the are of the pen.

2 * x + l = 80 so l = 80 – 2 * x

A = x * l
substitue for l:
A = x * (80 – 2 * x) = 80 * x _ 2 * x^2

dA/dx = 80 – 4 * x
When A is maximum, dA/dx = 0:
0 = 80 – 4 * x
4 * x = 80
x = 20
and since l = 80 – 2 * x:
l = 40 feet.

Pen and Ink – Fence Post

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CHICKEN – Speckled Sussex Fowl by fence Photo Mugs

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Fence

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