Mathematical Problem

Scenario:
There are 7 people, identified as persons 1 through 7, at destination X. There are three vehicles, A, B, C, of which the drivers are persons 1, 2, 3, respectively. The drivers can only drive their own car, and persons 4 through 7 cannot drive. All 7 people need to get to destination Z, but person 1 and person 4 need to go to destination Y first. Only two cars can go to destination Z, with the remaining car to be left at destination Y. Cars A and B can only fit five people, but car C can fit six. All materials necessary for arrival at destination Z are in the trunk of car A. In addition, there is urgency for person 5 to arrive at destination Z as soon as possible, with all the materials.

Problem:
a) What combination of persons, cars, events, and travelling routes results in an optimized solution?
b) How long does it take the seven people involved to decide on the answer to part a) above?

I love my family =)