A trolley conveyor serves four workstations. There are 543 carriers, equally spaced around the conveyor. The material flow patterns for the workstations are as follows:

{ f1(n)}  (0, 0, 3, 2, 0, 0, 0, 3, 2, 0, 0, 0, 3, 2, ...)

{ f2(n)}  (3, 0, 3, 0, 3, 0,3, 0,3, 0,3, 0, ...)

{ f3(n)}  (3, 0, 4, 0, 2, 0, 4, 0, 2, 0, 4, 0, ...)

{ f4(n)}  (0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, ...)

a. Given the patterns, what is the smallest period?

b. Can general sequences be accommodated? If so, why? If not, why not?

c. Can steady-state operations be achieved? If so, why? If not, why not?

d. Is conveyor compatibility guaranteed for all values of k not an integer multiple of the period of the material flow patterns? If so, why? If not, why not?