SOLUTION: A farmer has 336 running feet of fence and wishes to form a rectangular pasture. one side of the pasture will be bounded by a very long wall, so no fencing material will be needed

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Question 324005: A farmer has 336 running feet of fence and wishes to form a rectangular pasture. one side of the pasture will be bounded by a very long wall, so no fencing material will be needed for that side of the pasture. what should the dimensions of the pasture be if the area of the pasture is to be the largest possible?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
For a rectangle,
A=L%2AW
For the fencing,
L%2BW%2BW=336
L%2B2W=336
L=336-2W
Substitute into the area equation,
A=L%2AW=%28336-2W%29W
Now area is only a function of x, take the derivative and set it equal to zero.
A=-2W%5E2%2B336W
dA%2FdW=-4W%2B336=0
4W=336
W=84ft
Then from above,
L=336-2%2884%29=168ft
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The 168' x 84' rectangle will give you a maximum area of 14,112 sq. ft.