You will build two rectangular pens next to each other, sharing a side. you haves total of 384 feet of fence to use. find the dimension of each pen such that you can enclose the maximum area. the length of each pen (along the wall that they share) should be ? the width of each pen should be is ? the maximum area of each pen is ?

Answers
1). 96 units
2). 96 units
3). 9216 〖units〗^2

Explanations
Let the length of the pen be X.
We have been given the perimeter as 384.
Perimeter =2(l+w)
So, 384=2(x+w)
=192=x+w
W=192-x
Length = X and width = (192 – X)
Area =x(192-x)=192x-x^2
To get the maximum area, we equate the first derivative of the area (A) to zero.
A=192x-x^2
dA/dx=192-2x=0
2x=192
x=96
But width = 192 – X =192 – 96 = 96.
Maximum area =length×width
Maximum area=96×96=9216 〖units〗^2

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