Question

You have 1200 feet of fencing and you want to make two fenced in enclosures by splitting one enclosure in half. What are the largest dimensions of this enclosure that you could build?

Answer 1

\(3x+2y=1200\)

solve for \(y\) via
\[2y=1200-3x\]
\[y=600-\frac{3}{2}x\] area is \[A=xy=x(600-\frac{3}{2}x)=600x-\frac{3}{2}x^2\]
max is at the vertex, use \(-\frac{b}{2a}\) as before this time with \(a=-\frac{3}{2},b=600\)