Question

Can you guys help please im so confused

Answer 1

a) see below

b) 40x20 meters

Explanation:

Write down what you know:

- The area of the enclosure is length*width, so

`A = x \cdot y`

- The length of the fencing is 80 meters, so

`2y + x = 80`

Now we have to combine these two equations above, and get rid of y in the process.

First rewrite the second as:

`y = 40 - \frac12 x`

Then substitute for y in the first:

`A = x (40 - \frac12 x) = 40x - \frac12x^2`

b) To maximize A, find the zero of the first derivative:

`A'(x) = 40 - x = 0 \implies x=40`

So y = (80-40)/2 = 20 meters.