Calculus Question: A rancher plans to make four identical and adjacent rectangular pens, each with an area of 16m^2. What are the dimensions of each pen that minimize the amount of fence that must be used?

Question

campbell_st · Answer

ok... will start with area of 1 pen

A = length x width    or A = lw

so 16 = lw

so let w = 16/l

Perimeter P = 2l + 2w

or substituting 

               P = 2l + 16/l

you now need to find the 1st derivative

               dP/dl  

and then let it equal zero and solve

anonymous · Answer

Thanks!

campbell_st · Answer

I thin you'll find each pen needs to be a 4x4 square... so the total fencing is 48m