Rady grilled cheese is the most. Popular lunch spot on campus. During lunchtime, they are extremely busy. The manager 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 leave instead, presumably both frustrated and hungry.

Focusing on all arrivals, the potential demand is as follows

Time . Customers/minute

11 am - 12 pm = 9

12 pm - 12;15 pm = 11

12;15 pm- 12;30 pm = 8

12;30 pm - 12;55pm = 6

After 12;55 pm = 0

Currently she employs 7 students at a rate $15/hr to work from 10 am until 2pm. By contract, students 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 one minute to see one customer. Note that while customers eventually stop arriving, all customers who are waiting to get processed until everyone has been served.

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

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