I have theoretical problem about trains. I think it can be solved with graph theory, but I am not really good at math. Can you help me figure this out?
Train must go from A to B. There are many rail routes it can take. It must pay a pass fare to use the a route. They all differently charged. Each route leads to station. Each station pays train to visit station, but payments are also different. Goal is to arrive at B via route that makes most money.
For example, if A to B had 2 routes:
Route one A to A1 train must pay $100, A1 pays $1000 for train to visit A1 to A2 train must pay $800, A2 pays $2000 for train to visit A2 to B tain must pay $200
Train makes $1900.
Route two A to C1 train must pay $10, C1 pays $100 for train to visit C1 to C2 train must pay $5, C2 pays $200 for train to visit C2 to B train must pay $100
Train makes $185
We should pick route two because it train makes most money.
We have many routes to chose from in our actual problem.