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?
CALC - MathMate, Saturday, May 29, 2010 at 10:09pm
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
Differentiate with respect to x:
dL/dx = 3 - 2A/x²
To get minimum length,
dL/dx = 0
3 - 2A/x² = 0
Check that d²L/dx²>0 for L to be a minimum.
Calculate the length of fence required.
CALC - Adam, Sunday, May 30, 2010 at 1:21am
thank you so much for the clear explanation. i really understand how to do the problem now! i appreciate it!
CALC :) - MathMate, Sunday, May 30, 2010 at 8:34am
CALC - Kamsan, Saturday, November 12, 2011 at 9:17pm
what is the answer of this question?