Herr Cutter has run his barber shop from the same location for nearly 25 years. He opens his shop at 8.00 am each week day morning. He enjoys the relaxed working environment, the regular hours and the opportunity to visit with his customers. Over the years he has built a reliable clientele. He is a fine barber who takes pride in his work. He has observed however that in recent years his new customers are much less like to return as in early years. He attributes this to decreasing tolerance for waiting. He is considering whether to hire an assistant. He has been able to collect data on arrivals and service times over a number of days, and figures are summarized below.

Time Between Arrivals(mins) Probability Service Time (mins) Probability

20 0.2 15 0.3

25 0.3 20 0.35

30 0.35 25 0.35

35 0.15

Required

a) Construct the appropriate random number mappings for the random variables starting

from 00 . (3 marks)

b) Simulate 10 customers arriving at the using the random numbers given below. (12

marks)

c) What is the average time a customer waits for service? (1 mark)

d) What is the average time a customer is in the system (wait plus service time) (2 marks)

e) What is the percent of time Cutter is busy with customers? (2marks)

Random Numbers To Be Used in the Simulation

Customer 1 2 3 4 5 6 7 8 9 10

Interarrival time 0.08 0.87 0.15 0.04 0.52 0.46 0.96 0.10 0.02 0.76

Service Time 0.72 0.46 0.96 0.00 0.27 0.73 0.76 0.25 0.11 0.47

Use the following headings to complete the simulation

Customer

RN

Time Between Arrivals

Arrival Time

Begin Service

Wait for service

RN

Service Time

End Service

Time in System