You're out to make some money, so you look into it.
Some guy has 26 rocks, weighing from 1 to 26 pounds, inclusive, not necessarily distinct.
The stones each weigh a whole number of pounds, and the job is to label all the stones with their correct weight.
You have a balance - you know the kind - that gives one of three outcomes for the Left and Right pans:
You call the warehouse and find that whole-numbered weights cost $10 apiece and arbitrary-numbered weights cost $12 each.
Given that you want the job if you can clear $20 profit, what should you bid?