SOLUTION: Farmer Fred wants to fence in a rectangular pasture that is bordered on one side by a river. He plans to use 7200 feet of fence to enclose the other three sides . What should the d

Algebra ->  Test -> SOLUTION: Farmer Fred wants to fence in a rectangular pasture that is bordered on one side by a river. He plans to use 7200 feet of fence to enclose the other three sides . What should the d      Log On


   

Question 889070: Farmer Fred wants to fence in a rectangular pasture that is bordered on one side by a river. He plans to use 7200 feet of fence to enclose the other three sides . What should the dimensions of the pasture be if the enclosed area is to be maximum?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let the side parallel to the river be X and the other side Y.
X%2BX%2BY=7200
2X%2BY=7200
The area would then be,
A=XY
Substitute for Y using the perimeter equation,
Y=7200-2X
A=X%287200-2X%29=7200X-2X%5E2
To find the extrema, differentiate with respect to X and set the derivative equal to zero.
dA%2FdX=7200-4X=0
X=7200%2F4
highlight%28X=1800%29
Then,
Y=7200-3600
highlight%28Y=3600%29