Asked Oct 26, 2019

 A rancher wants to fence in an area of 2500000 square feet in a rectangular field and then divide it in half with a fence down the middle, parallel to one side.

What is the shortest length of fence that the rancher can use?


Expert Answer

Step 1

Let length of the sides are x and y. And the middle fence is parallel to x side.

So total fence needed = 3x+2y


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у X X х У

Step 2

Given area = 2500000 square feet 

So, xy= 2500000

y=2500000 / x

Plug this in the total perimeter. Then find dP/dx


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P= 3x+2y 2500000 P= 3x+2 X 5000000 P-3x+ X dP =3- dx 5000000 x2

Step 3

For minimum perimeter dP/dx=0 , from there w...


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5000000 3- =0 x2 5000000 =3 x2 5000000 x2= 3 5000000 5 x=1000 3 1000 15


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