Hello, bsalerno !
A rancher wants to fence in an area of 3,300,000 square feet in a rectangular field
and then divide it in half with a fence down the middle parallel to one side.
What is the shortest length of fence that the rancher can use?
Code:
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The constraint is the area: \(\displaystyle \,A\:=\:xy\:=\:3,300,000\;\;\Rightarrow\;\;y \,=\,\frac{3.300,000}{x}\;\)
[1]
The amount of fencing is: \(\displaystyle \,F\:=\:2x\,+\,3y\;\)
[2]
Substitute
[1] into
[2]: \(\displaystyle \:F\;=\;2x\,+\,3\left(\frac{3.300,000}{x}\right)\)
Therefore: \(\displaystyle \,F \;=\;2x\,+\,9,900,000x^{-1}\,\) is the function to minimize.
