Q$2.$American Vending Inc supplies vended food to a large university. Because students often kick the machines out of anger and frustration, management has a constant repair problem. The machine breakdown on an average of $3$ per hour and the breakdowns are distributed in a Poisson manner. Downtime costs the company $$25$ per hour per machine and each maintenance worker gets $$4$ per hour. One worker can service machines at an average rate of $5$ per hour, distributed exponentially: two workers together can service $7$ per hour and a team of three workers can do $8$ per hour.

What is the optimal maintenance crew size for servicing the machines?