SOLUTION: A college is planning to construct a rectangular parking lot on land bordered on one side by a highway. The plan is to use 600 feet of fencing to fence off the other three sides. W

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A college is planning to construct a rectangular parking lot on land bordered on one side by a highway. The plan is to use 600 feet of fencing to fence off the other three sides. W      Log On


   

Question 1062015: A college is planning to construct a rectangular parking lot on land bordered on one side by a highway. The plan is to use 600 feet of fencing to fence off the other three sides. What dimensions should the lot have if the enclosed area is to be a​ maximum?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The perimeter for 3 sides is
+P+=+2W+%2B+L+
+L+ is the side parallel to hwy
+W+ is perpendicular to hwy
--------------------------------
+P+=+600+ ft
+600=+2W+%2B+L+
+L+=+600+-+2W+
-------------------
The area +A+ is:
+A+=+L%2AW+
+A+=+%28+600+-+2W+%29%2AW+
+A+=+-2W%5E2+%2B+600W
--------------------------
+W%5Bmax%5D+ is found by the formula
+W%5Bmax%5D+=+-b%2F%282a%29+
+a+=+-2+
+b+=+600+
+W%5Bmax%5D+=+-600%2F%282%2A%28-2%29%29+
+W%5Bmax%5D+=+150+ ft
and
+L+=+600+-+2W+
+L+=+600+-+2%2A150+
+L+=+600+-+300+
+L+=+300+
---------------
The lot is 150 by 300 ft2
Plug this result back into equation
to find +A%5Bmax%5D+
+A%5Bmax%5D+=+-2%2A150%5E2+%2B+600%2A150+
+A%5Bmax%5D+=+-2%2A22500+%2B+90000+
+A%5Bmax%5D+=+-45000+%2B+90000+
+A%5Bmax%5D+=+45000+ ft2
------------------------------------
Here's the plot of +A+ as function of +W+
+graph%28+400%2C+400%2C+-50%2C+350%2C+-5000%2C+55000%2C+-2x%5E2+%2B+600x+%29+