some question must be prepared using an R markdown by showing all R code to generate the results

A service center consists of two servers, each working at an exponential rate of two services per hour. Customers arrive at a Poisson rate of three per hour, but the service center has the capacity of at most six customers (in service and in queue). (a) Write the instantaneous transition rate matrix R for the system. (7 marks) (b) With the approximation e" =(1+R) and n = 10 x,, determine the probability that there is still no customer in the system after an hour from the initial start time. (7 marks) (c) Determine the long-run probabilities. (4 marks) In terms of the long-run probabilities, (d) what fraction of potential customers enter the system? (1 mark) (e) what fraction of potential customers that are lost? (1 mark)