Final answer:
Ameren Illinois should use the Vehicle Routing Problem Route to optimize the collection of meter readings in Urbana, as it provides efficiency and covers all necessary customer locations.
Step-by-step explanation:
For Ameren Illinois to find the best route to collect meter readings from all residential customers in Urbana, they should use the Vehicle Routing Problem (VRP) Route. This type of network analysis is specifically designed to optimize routing for multiple vehicles visiting a set of locations with constraints, such as the total number of meters to be read and the sequence of visits. The VRP takes into account the most efficient path that minimizes distance or time while ensuring that all customer meters are read.