Expert: Paul Klarreich - 10/21/2010

Question
A rectangular field is to be enclosed on four sides with a fence.  Fencing costs $8
per foot for two opposite sides, and $3 per foot for the other two sides.  Find the
dimensions of the field of area 820ft^2 that would be the cheapest to enclose.

Answer
Questioner:   Ashley  
Country:  United States
Category:  Calculus
Private:  No
 
Subject:  Calculus
Question:  A rectangular field is to be enclosed on four sides with a fence.  Fencing costs $8 per foot for two opposite sides, and $3 per foot for the other two sides.  Find the dimensions of the field of area 820ft^2 that would be the cheapest to enclose.
 
Let W = width.
   L = length

Then C = 8*2*W + 3*2*L = 16W + 6L is the cost

But LW = 820, so W = 820/L

C = 16(820/L) + 6L

Do the arithmetic, differentiate, set that = 0, solve.

First check:

You will probably find this problem in  
 
http://en.allexperts.com/q/Calculus-2063/2009/11/Maximum-

minimum-problem-41.htm