Posted by Mysty on Thursday, May 19, 2011 at 1:13am.
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?

Algebra 2  drwls, Thursday, May 19, 2011 at 6:33am
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.
Answer This Question
Related Questions
 math  A farmer with 2000 meters of fencing wants to enclose a rectangular plot ...
 Math  A farmer with 8000 meters of fencing wants to enclose a rectangular plot ...
 Algebra  Farmer Ed has 9,000 meters of fencing, and wants to enclose a ...
 algebra  Farmer Ed has 9 comma 0009,000 meters of fencing, and wants to ...
 intermediate algebra  A farmer with 3000 feet of fencing wants to enclose a ...
 Pre calc  A farmer with 2000 meters of fencing wants to enclose a rectangular ...
 Precalculus  A farmer with 10000 meters of fencing wants to enclose a ...
 Calc.  Please help solve this, A farmer has 600m of fence and wants to enclose ...
 Math(HELP!)  A farmer has 120 feet of fencing to enclose a rectangular plot for...
 Math  A farmer uses 1034 meters of fencing to enclose a rectangular region and ...
More Related Questions