Grilled Cheese is the most popular lunch spot on campus. During lunchtime, they are extremely busy. The manager, Tamia, says she has seen customers who show up and simply leave when they see how busy it is. Employing a student, they collected data and learned that whenever there are 60 customers waiting in line, that is when they see some customers opting not to wait and leaving instead, presumably both frustrated and hungry.

Focusing on all arrivals, the potential demand is as follows:

Time Customers/minute

11:00am - 12:00pm 9

12:00pm - 12:15pm 11

12:15pm - 12:30pm 8

12:30pm - 12:55pm 6

After 12:55pm 0

Currently, she employs 7 student workers at a rate $15/hr to work from 10:00am until 2:00pm. By contract, student workers must be given a 4 hour shift and so she has workers help with preparation and clean-up in addition to serving customers during lunchtime. It takes a worker 1 minute to serve 1 customer. Note that while customers eventually stop arriving, all customers who are waiting continue to get processed until everyone has been served.

i) Given a maximum of 60 customers waiting and 7 workers, on average how long does a served customer wait prior to being served?

ii) The profit margin is $1 per served customer. How many student workers should she employ to maximize profits? Note that every worker must be hired for the entire shift and is therefore paid $60.