Question

A rectangular chicken pen is constructed. The back of the pen is an existing corrugated iron fence and the remaining three sides will be made from a single roll of chicken wire 80m long. What is the maximum area possible in which to feed using optimization using derivatives?

Answer 1

\[A = x(80-2x) = 80x-2x^{2}\]\[\frac{dA}{dx} =80 - 4x\]To maximize, solve for 0:\[0 = 80-4x\]\[80=4x\]\[20=x\]
So the maximum area would be (by plugging 20 in for x in the area equation):
\[80(20)-2(20)^{2} = 800m^{2}\]