Asmall textile company is working with 4 machines each of which breaks down with exponential interarrival times with mean 3 days. there are two repairmen in the maintenance department each of which repairs the broken machines with a mean of 2 days.

a) model the number of working machines as ctmc (steady state probabilities for 0,1,2,3,4 are 0.051,0.153,0.306,0.357,0.131)
b) model the number of broken machines as ctmc
c) what is the proportion of time all machines are working
d) what is the proportion of time both repairmen are busy
e) what is average number of machines broken and working