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## Answers

**Optimization and public transit fit well together. The rotations of buses and subways, and the schedules of their crews are nowadays commonly computed by optimization algorithms. Vehicle and crew scheduling lead to classical combinatorial optimization problems on network flows and path covers that are nowadays well understood. A solid theory and powerful algorithms have led to the development of mathematical vehicle and crew “optimizers”. These are on a mature level and available within the leading software systems for public transit companies**

the numbers are used in communication by money,calender,length of an object etc.