Algebra 2
posted by Mysty .
A farmer wants to enclose three sides of a rectangular area that borders a creek. He has 2400 meters of fencing material. What is the maximum area that can be enclosed by the fence?

Let L be the length of fence parallel to the river.
A = L*(2400L)/2 = 1200L  L^2/2
dA/dL = 0 = 1200  L (using calculus)
L = 1200 m for maximum A
Amax = 1200*600 = 720,000 m^2
You can get the same answer by completing the square.
A = (1/2)(L^2 2400L + 1,440,000) + 720,000
= (1/2)(L1200)^2 + 720,000
That obviously has a maximum value when L = 1200.
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