Find the dimensions of the rectangular corral producing the greatest enclosed area given 300 feet of fencing.

Answer 1

300/4 = 75 feet by 75 feet

with Area = 75^2 = 5625 square feet

A = Lw

P = 2L +2w = 300

L +w = 150

L = 150-w

A = (150-w)w = 150w -w^2

tale the derivative and set = 0

A' = 150 -2w = 0

w = 75 feet

L = 150-75 = 75 feet