math for precal

Question

Farmer Ed has 450 meters of​ fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the​ river, find the length and width of the plot that will maximize the area. What is the largest area that can be​ enclosed?

Answer 1

dimensions 112.5 by 225 meters maximizes Area

max Area = 112.5x225 = 25,312.5 square meters

A=LW = (450-2W)W = 450W-2W^2

take the first derivative and set = 0

A' = 450-4W =0

W = 225/2 = 112.5 meters wide

L = 450-225 = 225 meters long