Writing Homework Help

I’m working on a philosophy discussion question and need an explanation to help me learn.

A healthy man walks into a doctor’s office and the doctor discovers that she can save five people who would otherwise die by killing the healthy man and using his organs to replace damaged organs in the other five people.  Utilitarianism says, kill the man to save the other people since that would allow for the greatest happiness for the greatest number. This seems to go against what most people would think of as one of our most fundamental ethical beliefs, the sanctity of the individual.  Does this fatally undermine utilitarianism?  Can the distinction between act and rule utilitarianism save utilitarianism? Can Pojman’s defense of utilitarianism save it?

Readings: John Stuart Mill-Utilitarianism and  Louis P. Pojman-Strengths and Weaknesses of Utilitarianism