So I've taken Linear Programming 101.
I've read my textbook, took the test and all that, and - besides all the theory, the nice algebraic interpretations, etc - I've encountered a lot of textbook examples of linear programming problems.
You know, the usual, the diet problem, the transportation problem, the usual "a factory makes 300 screws and 400 bolts a day, McGyver is trapped in the factory and..." problem.
I wonder if there is some interesting example beyond that from real life or puzzles/card/board games that can be interpreted/modelled as a nice, elegant, perhaps even beautiful (but still nice and simple) linear programming problem.
I can't think of any, can you?
Bonus points if it uses duality.
I don't think I want to see the complete model, unless a lot of thought is required, though - you could as well leave me the fun of that or maybe just throw me a clue :)
Thanks!
Linear programming is widely used in all sorts of fun transportation problems. These problems are not simple, but they are useful and interesting. An example off the top of my head: how do you effectively allocate bikes or cars as a public resource?
Publicly available papers:
Balancing Bike Sharing Systems with Constraint Programming
Decision support for tactical resource allocation in bike sharing systems
Locating Stations for Bicycle-Sharing Schemes
Balancing Bicycle Sharing Systems: A Variable Neighborhood Search Approach?
The vehicle relocation problem for the one-way electric vehicle sharing
Optimizing Locations for a Vehicle Sharing System