Answer :
The area enclosed is (2x)(600-2x).(2x)(600−2x)=1200x−4x2
In order to maximize we need the derivative to be equal to 0.y′=1200−8x=0
1200=8x
x=150
Therefore the sides for maximum area are 150*300.
The area is: 45000
In order to maximize we need the derivative to be equal to 0.y′=1200−8x=0
1200=8x
x=150
Therefore the sides for maximum area are 150*300.
The area is: 45000
Answer:
Area is 45000 square feet.
Step-by-step explanation:
Let x be the length of fenced side parallel to the river side.
Let y be the length of other two sides.
Then,
[tex]x+ 2y 600[/tex]
So, we get [tex]x=600-2y[/tex]
Area of this rectangle = xy
= [tex]y(600-2y)[/tex]
[tex]x=-2y^{2}+600y[/tex]
Now attached is the graph of the area function, which is a parabola opening downward.
We can see ta the maximum area occurs when y=[tex]-600/[2(-2)][/tex] = 150
And [tex]x = 600-2(150)[/tex]
x =[tex]600-300=300[/tex]
Therefore, to maximize the area, the side parallel to the river is to be 300 feet long, and the other two fenced sides should be 150 feet long.
The area is = [tex]300\times150= 45000[/tex] square feet.
