Alex has 520 yards of fencing to enclose a rectangular area.

a retangle that maximises the enclosed area has a length of _ yards and a width of _ yards.

the maxium area is yards

The first thing we are going to do for this case is define variables.

We have then:

w: width

l: length

The perimeter is given by:

The area is given by:

The area as a function of a variable is:

Rewriting we have:

To obtain the maximum area, we derive:

We equal zero and clear the value of w:

Then, the length is given by:

Finally, the maximum area obtained is:

A retangle that maximizes the enclosed area has a length of 130 yards and a width of 130 yards.

The maxium area is 16900 square yards

B.
There is a 10 cent difference in the cost per minute, which is where the -.10x comes from. There is also a 10 dollar difference in the start up fees, which gives you the +10. 

So, if you were to choose Cell phone company Z, you would lose 10 cents per minute, but save gain 10 dollars at the beginning. -10x+10