You operate a shop in a large city, specializing in repairing small household items.  You serve a large customer base, the average number of items dropped off per day for repair is 61.2, and you charge your customers $40 per item.

You pay each worker  in the shop $100 per day base pay, plus $15 per item repaired.  A worker can repair up to 7 items per day.  However, each worker has an independent 3% chance of not showing up for work on any given day (in which case they are not paid).

You have an "always ready in one day" customer service policy, so if you do not have enough workers to repair all the items dropped of on a given day, you subcontract the work to another firm. However, doing so costs you $60 per item.

You are wondering how many workers to keep on staff: 8, 9, 10, 11, or 12 (assume that if a worker does not show up for work, it is not possible to find a replacement on short notice).  Which number of workers gives the best profit?  With that many workers, what is the average number of subcontract jobs per day?