You are running a small manufacturing shop with plenty of workers but with a single milling machine. You have to produce n items; item i requires mi machining time first and then pi polishing time by hand.
The machine can mill only one object at a time, but your workers can be polishing in parallel as many objects as you wish.
You have to determine the order in which the objects should be machined so that the whole production is finished as quickly as possible.
Prove that your solution is optimal.