farmer ed has 140

Question

farmer ed has 140 feet of fencing, and wants to enclose a rectangular plot that borders on the 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

140 = 2W + L

L= 140-2W

Area = A = LW = (140-2W)W = 140W -2W^2

take the derivative and set = 0

A'(W) = 140 -4W =0

4W = 140

W = 140/4 = 35 feet wide

L= 140-2W = 140-70 = 70 feet wide

35 by 70 feet maximizes the area

A= LW = 70(35) = 2,450 square feet = maximum area