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?

Answer 1

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.

Answer 2

thank you so much for the clear explanation. i really understand how to do the problem now! i appreciate it!

Answer 3

You're welcome!

Answer 4

what is the answer of this question?