One might suspect that fast enough on specific problems for approximate solutions that still make/save a lot of money might also be welcome. Ah, perhaps not!
E.g., in NYC, two guys had a marketing resource allocation problem, tried simulated annealing, and ran for days before giving up.
They sent me the problem statement via email, and in one week I had the software written and in the next week used the IBM OSL (Optimization Subroutine Library) and some Lagrangian relaxation. In 500 primal-dual iterations with
600,000 variables
40,000 constraints
found a feasible solution within 0.025% of optimality.
So, I'd solved their problem (for practical purposes, the 0.025% has to count as a solving) for free.
They were so embarrassed they wanted nothing to do with me. We never got to where I set a price for my work.
The problem those two guys had was likely that, if they worked with me, then I would understand their customers and, then, beat the guys and take their customers. There in NYC, that happened a second time.
If a guy is in, say, the auto business, and needs a lawyer, the guy might want the best lawyer but will not fear that the lawyer will enter the auto business as a powerful competitor. Similarly for a good medical doctor.
For an optimization guy saving, say, 5% of the operating costs of a big business, say, $billion in revenue a year, all the management suite will be afraid of the guy getting too much power and work to get him out -- Goal Subordination 101 or just fighting to retain position in the tribe.
After having some grand successes in applied math where other people had the problem but then being afraid that I would be too powerful, I formulated:
If some technical, computing, math, etc. idea you have is so valuable, then start your own business exploiting that idea -- of course, need a suitable business for the idea to be powerful.