From a point within the utilities possibilities frontier,

A) movement to another point within the frontier can only increase one person's utility, but not both people's utility.
B) it is possible to find another point within the frontier that generates higher utility for both people.
C) it is possible to find another point within the frontier that involves higher output of both goods.
D) any move to another point within the frontier will necessarily decrease someone's utility.

The possibilities frontier represents the maximum amount of output of two goods that can be produced with the given resources and technology. If a point within the frontier is chosen, it means that resources are used efficiently to produce the optimal combination of goods. Therefore, it is possible to find another point within the frontier that generates higher utility for both parties by reallocating resources in such a way that produces more of one good without giving up too much of the other good. This would lead to a more preferred point for both parties.