Knapsack problems, some simple scheduling problems, even the travelling salesman problem.
Many problems in business and manufacturing fit this bill. Optimal product mix, optimal routing, choosing the best spot for a warehouse, scheduling employees, constructing an investment protfolio, coming up with a diet that fits certain criteria, etc.
I even remember a practice problem from uni where we had to optimally distribute songs on two sides of a tape album (it was an old professor), satisfying constraints such as “each side should have a ballad” and “each side has at most x minutes of running time”.
You can do this with regular coding too, but if you can easily construct a certain kind of mathematical model of your problem, you can easily solve it with linear programming.
Many problems in business and manufacturing fit this bill. Optimal product mix, optimal routing, choosing the best spot for a warehouse, scheduling employees, constructing an investment protfolio, coming up with a diet that fits certain criteria, etc.
I even remember a practice problem from uni where we had to optimally distribute songs on two sides of a tape album (it was an old professor), satisfying constraints such as “each side should have a ballad” and “each side has at most x minutes of running time”.
You can do this with regular coding too, but if you can easily construct a certain kind of mathematical model of your problem, you can easily solve it with linear programming.