Two cities are located in the xy-plane at the points A(3,8) and B(6,3). A company wishes to place a factory on a road between the cities at A and B. It is determined
that the company can make the most money if it places the factory exactly halfway
between A and B. However, due to environmental hazards produced by the factory,
it is safe for the people living in A and B only if the factory is located exactly 2/3
of the distance from A going toward B. Find the coordinates of the point where the
factory should be placed to ensure the most ethical outcome. Explain your decision.