How many barbers a big city supports

Estimate the number of barbers working in a large city.

For a city of about 8 million, roughly 10,000 to 15,000. About $4$ million males; say $75\%$ use a barber, about every $5$ weeks, giving roughly $30$ million cuts a year. A barber doing about $12$ cuts a day for $250$ days handles about $3000$ a year, so about $10{,}000$ barbers, more if many work part-time. Show the chain of assumptions and which ones drive the answer.