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A farmer needs to enclose an area of 800 square feet for an animal pen. one side of the fence is electric which is 3 times more expensive than regular fences. Find the dimensions of the cheapest design.

Answer :

raphealnwobi

Answer:

20ft by 40ft

Step-by-step explanation:

The area of the fence is  800 ft². Let x represent one side of the fence and y the other side of the fence, hence:

xy = 800      (1)

The cost of fencing (C) is:

C = 3x + x + y + y

C = 4x + 2y      (2)

From xy = 800, y = 800/x. Substituting in equation 2:

[tex]C = 4x +2( \frac{800}{x})\\\\Minimum \ cost\ is\ at\ C'=0\\\\Hence:\\ \\C'=4-\frac{1600}{x^2} \\\\4-\frac{1600}{x^2} =0\\\\4=\frac{1600}{x^2} \\\\x=\sqrt{\frac{1600}{4} } \\\\x=20\ ft\\\\y=\frac{800}{x} =\frac{800}{20}=40\ ft[/tex]

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