CALC
posted by Adam on .
A rancher wants to fence in an area of 1500000 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?

Area to be fenced in, A = 1,500,000 sq.ft.
Width (shorter side) = x
Length (longer side) = A/x
Total length of fence, L
= 3x+2(A/x)
Differentiate with respect to x:
dL/dx = 3  2A/x²
To get minimum length,
dL/dx = 0
3  2A/x² = 0
x=sqrt(2A/3)=1000 ft.
Check that d²L/dx²>0 for L to be a minimum.
Calculate the length of fence required. 
thank you so much for the clear explanation. i really understand how to do the problem now! i appreciate it!

You're welcome!

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