SOLUTION: A rectangular field will be fenced on all four sides. Fencing for the north and south sides costs $9 per foot and fencing for the other two sides costs $8 per foot. What is the max

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Question 829718: A rectangular field will be fenced on all four sides. Fencing for the north and south sides costs $9 per foot and fencing for the other two sides costs $8 per foot. What is the maximum area that can be enclosed for $4800?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +A+ = area of the field
Let +L+ = length of the field
Let +W+ = the width of the field
+A+=+L%2AW+
+4800+=+2%2A9%2AL+%2B+2%2A8%2AW+
+4800+=+18L+%2B+16W+
----------------------
I can say;
+L+=+A%2FW+
and substitute
+4800+=+18%2A%28+A%2FW+%29+%2B+16W+
Multiply both sides by +W+
+4800W+=+18A+%2B+16W%5E2+
+18A+=+-16W%5E2+%2B+4800W+
+A+=+%28-8%2F9%29%2AW%5E2+%2B+%28+2400%2F9+%29%2AW+
--------------------------------
This is a parabola with a maximum at +W%5Bmax%5D+=+-b%2F%282a%29+ where
+a+=+-8%2F9+
+b+=+800%2F3+
+W%5Bmax%5D+=+-%28+2400%2F9+%29+%2F+%28+2%2A%28+-8%2F9+%29+%29+
+W%5Bmax%5D+=+2400%2F16+
+W%5Bmax%5D+=+150+
and since
+A%5Bmax%5D+=+%28-8%2F9%29%2AW%5E2+%2B+%28+2400%2F9+%29%2AW+
+A%5Bmax%5D+=+%28-8%2F9%29%2A150%5E2+%2B+%28+2400%2F9+%29%2A150+
+A%5Bmax%5D+=+%28-8%2F9%29%2A22500+%2B+40000+
+A%5Bmax%5D+=+-20000+%2B+40000+
+A%5Bmax%5D+=+20000+ ft2
check answer:
+4800+=+18L+%2B+16W+
+4800+=+18L+%2B+16%2A150+
+4800+=+18L+%2B+2400+
+18L+=+2400+
+L%5Bmax%5D+=+133.333+
+A%5Bmax%5D+=+W%5Bmax%5D%2AL%5Bmax%5D+
+A%5Bmax%5D+=+150%2A133.333+
+A%5Bmax%5D+=+19999.95+
The error is due to rounding off