Answer in Calculus for Nicey #265842
A resort owner wants to enclose a beachfront area for swimming activities. Based on her plan, only 3 sides will be fence with 270 meter rope and floats, while the shoreline part will be open. Determine the dimension of the 3 sides of the rectangle that will give a maximum area.
Lets draw a picture
We have to find such value 0 < x < 270 that maximize the area of the blue rectangle. Let S be the area, then “S(x)=x*(270-2x)=270x-2x^2”
Lets find the critical points
“270-4x=0implies x =67.5”. Since to the left from x = 67.5 the value of S'(X) is positive, and to the right it’s negative, then x = 67.5 is the point of maximum
The sides of a rectangle is 67.5 and 270 – 2 * 67.5 = 135 meters and the area is“S(67.5)=270*67.5-2*67.5^2=9112.5” square meters