Problem 2: UoS has decided to install an air cleaning system in its precision engineering lab during the summer term. The lab will be unavailable to students during the installation. For this reason, the University does not want the installation to exceed 3 weeks.

The following table details the required activities. What are the earliest start and finish, latest start and finish, and slack of each activity? Which activities are critical? Will the project complete in 3 weeks?

Provide a network diagram for this problem. You can draw it by hand (neatly) and include its clear snapshot in your Word document. [10 Marks]

Activity	Description	Time Estimate (days)	Immediate Predecessor(s)
A	Building internal components	3	-
B	Modify roof and floor	4	-
C	Construct collection stack	3	A
D	Pour concrete and install frame	5	B
E	Build and connect ducts	7	C
F	Install control system	3	C
G	Install air pollution device	6	D,E,F
H	Inspection and testing	4	G

Problem 3: On average 8 customers arrive at an ATM every hour. On average, a customer uses the ATM for 5 minutes. Assuming Poisson distribution of the arrival rate and Exponential distribution of service times, what is the expected number of customers waiting to use the ATM (Lq) at a time, and what is the expected waiting time in the queue (Wq)? (Apply the single server queueing model. Maintain 3 decimal places. State the time unit for Wq) [2 Marks]