How would we use Utilitarianism to “solve” this dilemma?

How would we use Utilitarianism to “solve” this dilemma?
There are three basic propositions in standard Utilitarianism (Please be sure to listen to Mill’s audio lecture before joining this threaded discussion):

Actions are judged right and wrong solely on their consequences; that is, nothing else matters except the consequence, and right actions are simply those with the best consequences.
To assess consequences, the only thing that matters is the amount of happiness and unhappiness caused; that is, there is only one criterion and everything else is irrelevant.
In calculating happiness and unhappiness caused, nobody’s happiness counts any more than anybody else’s; that is, everybody’s welfare is equally important and the majority rules.
In specific cases where justice and utility are in conflict, it may seem expedient to serve the greater happiness through quick action that overrules consideration for justice. There is a side to happiness that can call for rushed decisions and actions that put decision-makers under the pressure of expediency.

Here is a dilemma for our class:

You are the elected district attorney. You receive a phone call from a nursing home administrator who was a good friend of yours in college. She has a waiting list of 3,000 people who will die if they don’t get into her nursing home facility within the next 3 weeks, and she currently has 400 patients who have asked (or their families have asked on their behalf) for the famous Dr. Jack Kevorkian’s (fictitious) sister, Dr. Jill Kevorkian, for assistance in helping them die. The 3,000 people on the waiting list want to live. She (the nursing home administrator) wants to know if you would agree to “look the other way” if she let in Dr. Jill to assist in the suicide of the 400 patients who have requested it, thus allowing at least 400 of the 3,000 on the waiting list in.

How would we use Utilitarianism to “solve” this dilemma?
How would we use cars-based ethics to “solve” this dilemma?
What ethics did your friend, the nursing home administrator, use in deciding to call you?
What ethics are you using if you just “look the other way” and let it happen?