The dilution math
If each step mixes one part of the previous solution into enough solvent to make F parts in total, the concentration falls by a factor of F every step. After n steps, the final concentration is C0 divided by F to the power n.
This model starts from an extract of 1,000 µg/mL, a round teaching value. Potency labs choose the factor and number of steps so the final sample lands inside the concentration range their chromatograph was calibrated to measure, then multiply the measured value back up by the total dilution.
Why robots, and why the time estimate is simplified
A robot repeats the same aspirate and dispense motions for hours without the drift and fatigue that hand pipetting brings, and it logs every transfer. This run time counts 8 moves per dilution step plus 2 per sample (tip on, aspirate, travel, dispense, mix, tip off, and a diluent fill) at about 4 seconds each. Real cycle times depend on volumes, mixing and the head; multichannel heads that work 8 or 96 wells at once cut the time dramatically.
Tips are counted as one fresh tip per transfer plus one for adding solvent to each sample's tubes. Labs track tip use closely because tips are a large share of consumable cost.