Create Point on a Polyline with a location that maximizes a function

Discussion created by isotopes on Oct 15, 2012
Latest reply on Nov 8, 2012 by gpw0976
I have a group of points that each has a value associated with them. I also have a polyline. I want to create a new point on that polyline which will be placed where the average value of each point divided by the average distance been each point to the new point on the line is the largest. Or put another way:

Find (x,y) on polyline with Maximum(average(values/distances))

I???m not sure how to do this with ArcGIS. I know how to get a solution using linear programming if the line was a straight line (or a function), but of course it???s a complicated line (actually several disconnected lines representing a fault).