i have a certain number of cars to rent.  each day this number changes
from 100 to 125.  this is a very price competitive product.  the
market and competitors adjust pricing on as often as an hourly basis. 
what formula could be used to maximize total revenue dollars.  ie; if
we have 100 cars to rent on a Tuesday, at what point (50,65 or 70
reservations) should we be able to increase our prices and by what %

Hi there,

It seems tough to devise a formula without any measure of how
customers will respond to increased prices. Are you saying that your
prices must necessarily be the same as those of competitors? (because
if yours were lower, you could raise them for more profit, and if they
were higher, then your customers would go to the competitor)

Regardless, it seems a "skim pricing" strategy would be most
appropriate in your situation. For example, go to <a
href="http://www.southwest.com">Southwest Airlines'</a> website and
choose a reservation more than 14 days in advance from a major city to
another, roundtrip, and you'll find that Southwest allocates a certain
amount of "cheap seats" to each flight. Once they're gone, there are
some almost-cheap seats, and so on until we get to the standard price.

You can do a similar thing with your rental cars, and just like
Southwest, you can use an infinite amount of levels. Yet without a
measure of what price consumers are willing to pay, exact numbers are
tough to come by. For example, using the information you gave, I don't
see any way to determine the anticipated number of cars rented at
$30/day and $50/day.

Another way to get rid of your "cheap seats" is Priceline.com, though
it is unlikely that they will work with you to get rid of excess
inventory unless you have a major brand name.

Hope this helps.