SOLUTION: CAN ANYONE HELP ME?? Minimum Cost A rectangular area adjacent to a river is to be fenced in; no fence is needed on the river side. The enclosed area is to be 1000 square feet. Fenc

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Question 969085: CAN ANYONE HELP ME?? Minimum Cost A rectangular area adjacent to a river is to be fenced in; no fence is needed on the river side. The enclosed area is to be 1000 square feet. Fencing for the side parallel to the river is $5 per linear foot, and fencing for the other two sides is $8 per linear foot; the four corner posts are $25 apiece. Let x be the length of one of the sides perpendicular to the river.
(a) Write a function C(x) that describes the cost of the project.
(b) What is the domain of C?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Area = +1000+ ft2
Let the length parallel to the river = +y+ ft
I can say:
+A+=+x%2Ay+
+y+=+A+%2F+x+
+y+=+1000+%2F+x+ ft
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The perimeter of the rectangular are is:
+p+=+2x+%2B+1000%2Fx++
+C%28x%29+=+%28+2x+%29%2A8+%2B+%28+1000%2Fx+%29%2A5+%2B+4%2A25+
+C%28x%29+=+16x+%2B+5000%2Fx+%2B+100+
-------------------------------
+x%2Ay+=+1000+
+x+ can be any number
Also +y+ can be any number
-----------------------------------
The domain is:
0 < C(x) < infinity
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Here's the plot of +C%28x%29+
+graph%28+500%2C+500%2C+-20%2C+150%2C+-100%2C+1500%2C+16x+%2B+5000%2Fx+%2B+100+%29+
After the curve takes a dip, it looks like a straight line almost
Hope this helps