SOLUTION: The problem is stated below. For the area LW=800, I isolated L, which is L=(800/W). Then I plugged this into the perimeter equation P=2(800/W)+2W -> P=(1600/W)+2W -> P=1600

Question 721031: The problem is stated below.
For the area LW=800, I isolated L, which is L=(800/W).
Then I plugged this into the perimeter equation
P=2(800/W)+2W -> P=(1600/W)+2W -> P=1600+2W^2
Then, derivative = 4W. But when I set the derivative to equal 0, W=0 which doesn't make sense.
I'm not sure where my error is. Could you please show me how you would solve it. Thanks in advance!
Here is the problem: "A rectangular field is to have an area of 800 m^2 and is to be surrounded by a fence. The cost of the fence is 12 dollars per meter of length. What is the minimum cost this can be done for?"
$________
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
A mistake is found in this part of your process:
"P=2(800/W)+2W -> P=(1600/W)+2W -> P=1600+2W^2"

So you are looking for derivative of perimeter, P, and you should be using . Derivative with regard to W should be (1600/W)' + 2. Should be derivative is . The first term would or could use Quotient Rule.
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