Answer:
a) see below
b) 40x20 meters
Step-by-step explanation:
Write down what you know:
- The area of the enclosure is length*width, so
[tex]A = x \cdot y[/tex]
- The length of the fencing is 80 meters, so
[tex]2y + x = 80[/tex]
Now we have to combine these two equations above, and get rid of y in the process.
First rewrite the second as:
[tex]y = 40 - \frac12 x[/tex]
Then substitute for y in the first:
[tex]A = x (40 - \frac12 x) = 40x - \frac12x^2[/tex]
b) To maximize A, find the zero of the first derivative:
[tex]A'(x) = 40 - x = 0 \implies x=40[/tex]
So y = (80-40)/2 = 20 meters.
