Asked 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?
Answers
Answered by
drwls
Let L be the length of fence parallel to the river.
A = L*(2400-L)/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)(L-1200)^2 + 720,000
That obviously has a maximum value when L = 1200.
A = L*(2400-L)/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)(L-1200)^2 + 720,000
That obviously has a maximum value when L = 1200.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.