1. The lab supervisor needs to establish a weekly schedule for the morning shift. Based on distributions of arrival times and service times, she has conducted a queuing analysis and found that the minimal number of lab technicians for each day is the following:

Each technician is also allowed to take 2 days off every week. Technicians prefer to have 2 consecutive days off. There are therefore seven possible schedules (Monday and Tuesday off, Tuesday and Wednesday off, Wednesday and Thursday off, etc.).
Formulate and solve an integer linear programming model that will determine the number of technicians for each one of the seven schedules while minimizing weekly cost and providing the necessary capacity and giving each lab technician 2 days off.
Hint: Define the decision variables as the number of technicians in schedule 1, 2, 3, …