Using Utilitarian principles what should a leader do if a lifeboat could only carry 20 people and there are 30?
Utilitarianism teaches us that the right action is the one that creates the greatest possible happiness for the greatest number of people. In other words, we have to measure how happy each course of action makes people (measuring both how many people are made happy and the intensity of their potential happiness) and choose the one that creates the greatest total happiness.
From a strictly utilitarian point of view, whoever is in charge of the lifeboat would need to look at the 30 people and pick those who are most likely to add to the general happiness of humanity. The 20 who are most likely to do this get to live. This would presumably include such things as deciding how many people would be saddened by the death of one person as opposed to another. It would also include considerations of what each person does for a living and how much their actions are likely to improve the lives of people in general.
Of course, these sorts of considerations are beyond the ability of any person to calculate. It might be best for whoever is in charge to ask for volunteers. This could allow some people to decide if they felt they should sacrifice themselves. If they did so, it might temper the grief felt by those who they leave behind. Those people could actually feel happy because their relative had acted so heroically. Thus, calling for volunteers might well avoid the problem of having to pick who lives and who dies.