A manufacturing system is comprised of two machines (a drilling machine and a laser cutting machine) working in series to process two part types (A and B). Assume that Part A arrive to the drilling machine according to a Uniform (2,6) minutes distribution and that Part B arrive to the drilling machine according to a Triangular (0.5,3,5) minutes distribution. Parts are drilled according to a first in first out (FIFO) queuing discipline. The drilling machine requires a fixed 2 minutes to process each part, regardless of type. All parts go immediately to the cutting process after exiting the drilling machine. There are two laser-cutting machines. Parts wait for the next available laser-cutting machine and are cut according to a last in first out (LIFO) queuing discipline. The processing time distribution at each laser-cutting machine is Exponential (4) minutes, regardless of part type. 

a) What is the average waiting time at the laser cutting machines? 

b) How many parts exited the system? 

c) What is the average number of parts waiting at the drilling machine? 

d) What is the maximum time a part spent in the system? 

e) What is the average utilization of the cutting machines over the eight-hour run? 

f) What is the average time a part spent in the system?