please can you solve for me this stochastic processes question, have received few very wrong answers, and there is no missing links or info in this. Thank you very much.

3. (a) During lunch hour, arrivals of customers at a pizza hut restaurant follows a Poisson process with the rate of 120 customers per hour. The restaurant has one line, with three workers taking food orders at independent services stations. Each worker takes an exponen- tially distributed amount of timeon average 1 minuteto serve a customer. Let X] denote the number of customers in the restaurant (in line and being serviced) at time t. Then, the process (Xi : t 2 0) is a continuous-time Markov chain. (i) Show that the process is a birth-anddeath process by giving the birth and death rates. [4 marks] (ii) Find the generator matrix of the above process. [5 marks] (iii) For each integer k 2 0, derive the longterm probability that there are k customers in the restaurant. [8 marks] (iv) Calculate the longterm probability that all three workers are busy. [6 marks] (v) Find the average number of customers in the restaurant in the long term. [7 marks] (b) A student support center has 3 tutors who help students with their home work. Students arrive at the center according to a Poisson process at rate A = 3 per hour. Each tutor's service time is exponentially distributed with average of 1/10 hours. Tutors' service times and student arrival times are independent. If all the tutors are busy when a student arrives at the center, the student will leave. Let Xi denote the number of tutors who are busy at time t. Determine its generator matrix and stationary distribution. [10 marks]