Mr. Larsson is an accountant who prepares final accounts for his clients. Work arrives at his office randomly at a rate of 8 per month. The times taken to complete the work form an exponential distribution with a mean of 3 days. There are 25 working days in each month.

Mr. Larsson is considering employing an apprentice to do the basic calculations on each job before he does the complicated parts. This should enable the completion of mean of 2 days, though the distribution will still be exponential.

(a) Describe the steps involved in taking a scientific approach to management problems.

(b) For the current situation and then with the employment of the apprentice calculate the following:

(i) Values for λ, μ and ρ

(ii) The queue length and waiting time for clients including and excluding the service time

(iii) The probability that there will be more than 2 customers waiting

(iv) The probability that a client will wait (including service) for more than 2 months to have his accounts completed