Answer:
150 ft x 300 ft
Step-by-step explanation:
Let x be the length of each of the two sides perpendicular to the river and y be the length of the size parallel to the river.
The total length of fencing is given by:
[tex]2x+y=600\\y= 600-2x[/tex]
The area of rectangular pen is:
[tex]A = xy\\A=x(600-2x)\\A= 600x -2x^2[/tex]
Finding the value of x for which the derivative of the area function is zero gives us the value of x needed to maximize the area:
[tex]\frac{dA(x)}{dx} =\frac{d(600x -2x^2)}{dx}\\0= 600 - 4x\\x= 150[/tex]
For x=150, the value of y is:
[tex]y= 600-2x=600-(2*150)\\y=300[/tex]
The dimensions that maximize the area are 150 ft x 300 ft.
