Consider: doing so goes against the Hypocratic Oath, which all doctors take, and which they live their lives by. It's their code of ethics, one of the key things that makes them what they are.
I think it's pertinent to decompose this problem into the 4 factors:
Ethically - it's absolutely wrong for a doctor to do that, there's no question. This has to be taken into account.
Legality - doesn't come into the picture in this scenario.
Utility - This is debateable, but it's probably going to create more happiness than it's taking away, and where Trust is probably basing his decision, and where most people in the Western world base their decisions.
Morality - Is where the problem lies. I don't personally think that it's a moral decision to choose who dies, even if you're saving more lives. It almost seems that you're trying to act as God, or as an ultimate judge. I personally couldn't live with making that decision, even if I'm saving more people.
I'm interested in hearing other opinions, though.