Any decision made implies a combination of prior over those values and risk tolerance.
If you treat budgeting as an optimization problem, you need forecasts, not priors.
I would also suspect that real-life business budgets will be hard to set as "rigorous optimization problems" because in reality you have discontinuities, nonlinear responses, and all kinds of funky dependencies between different parts of the budget.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
Notes for future OT posters:
1. Please add the 'open_thread' tag.
2. Check if there is an active Open Thread before posting a new one. (Immediately before; refresh the list-of-threads page before posting.)
3. Open Threads should be posted in Discussion, and not Main.
4. Open Threads should start on Monday, and end on Sunday.