I FOUND YOUR COMPLETE QUESTION IN OTHER SOURCES. PLEASE SEE ATTACHED IMAGE.
The perimeter is given by: P = 2 (2x) + 2 (y) Rewriting we have: P = 4x + 2y Substituting: 800 = 4x + 2y The area is: A = 2x * y We write the area as a function of x: A (x) = 2x * (400-2x) Rewriting: A (x) = 800x-4x ^ 2 We derive: A '(x) = 800-8x We match zero: 0 = 800-8x We clear x: x = 800/8 x = 100 feet We check that it is a maximum. For this, we look for the second derivative: A '' (x) = - 8 We evaluate x = 100 A '' (100) = - 8 <0 (is a maximum) We look for the other dimension: y = 400-2x y = 400-2 (100) y = 400-200 y = 200 feet Answer: The dimensions that should be used are that the enclosed area will be a maximum are: x = 100 feet y = 200 feet
