The owner of a motel has 5000 m of fencing and wants to enclose a rectangular plot of land that borders a straight highway. if she does not fence the side along the highway, what is the largest area that can be enclosed?
Accepted Solution
A:
The perimeter in this case is: y + 2x = 5000 The area is: A = x * y We rewrite the area: A = x * (5000-2x) A = 5000x-2x ^ 2 We derive: A '= 5000-4x We equal zero and clear x: 0 = 5000-4x 4x = 5000 x = 5000/4 x = 1250 We look for the other dimension: y = 5000-2x y = 5000-2 (1250) y = 5000-2500 y = 2500 Then, the area will be: A = (2500) * (1250) A = 3125000 m ^ 2 Answer: The largest area that can be enclosed is: A = 3125000 m ^ 2