What are the dimensions of a rectangular wall that can be constructed with 10,000 feet of brick that will maximize the area enclosed by that brick?

Question

The answers are:

A. 100 feet by 100 feet

B. 20 feet by 500 feet

C. 50 feet by 200 feet

D. 2,500 feet by 2,500 feet

Answer 1

Perimeter = 10,000 = 2(L+W)

5,000 = L+W

L + 5,000 -W

Area = LW = (5000-W)(W)

A = 5000W -W^2

take the derivative and set =0

A' =5000-2W = 0

2W =5000

W =2500 feet =Width

5000-1500 = 2500 feet = Length

maximum area =2500^2 = 6,250,000 ft^2

D is correct

max area for a rectangle with a fixed perimeter is a square

10,000/4 = 2500 feet = one side of the square

2500 by 2500