Question

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?

Answer 1

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

Answer 2

Thanks!

Answer 3

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