Suppose a psychedelic drug that is incredibly difficult to synthesize makes someone inhumanly good at problem solving, but only for a few minutes.
Further suppose one of the easiest ways to create this drug is to harvest human brains. They have to be extracted while the donor is still alive, though, as the delicate compounds coming from the brain become unusable rapidly after death.
According to utilitarianism, if that person uses their insane problem solving abilities to increase utility for others, and they're good enough at it with this drug, then we should throw the people who generate the least utility for others (e.g. the poor and disadvantaged, who usually have few resources to offer and little training or skill) into the brain ripper so that the remaining people can get the gains.
This example may seem absurd, but many others like it can be constructed. Spend a few minutes trying and you'll come up with some. This one took me thirty seconds, if that.
See "The Ones Who Walk Away From Omelas" by Ursula K. Le Guin for the canonical illustration of this problem.