$A rectangular garden plot is to be fenced off along the property line.$

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$A rectangular garden plot is to be fenced off along the property line.$

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Calculus

Jayellis00

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(a) The total area is
\[(1) A=LW=400.\]
(b) The cost of the fence is
\[(2) C=3L+2L+2W+2W=5L+4W.\]
(c) To inimize the cost, from equation (1) we get
\[L=\frac{400}{W}.\]
Substituting this in (2) we get
\[ C=5(\frac{400}{W}) +4W=\frac{2000}{W}+W.\]
Hence
\[C'(W)=\frac{-2000}{W^2}+1=0 \Rightarrow W^2=2000 \Rightarrow W=\sqrt{2000}.\]
Also
\[L=\frac{400}{W}=\frac{400}{\sqrt{2000}}.\]
So
\[W=\sqrt{2000} \text{and} L=\frac{400}{\sqrt{2000}}.\]

Erdos

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$A rectangular garden plot is to be fenced off along the property line.$

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