Question

ASAPP

youre managing an accountant firm during tax season and customers arrive at the rate of 12 per hour. You have 3 staff accountants and they typically take an average of 6 minutes to meet the customer, collect the paperwork, provide an initial assesment of the tax return and set up a follow up meeting. Given this information, which of the following describes the number of people waiting in the system and the total time (waiting in line and being serviced) a customer will wait in your office

a.) 0.0675/9 minutes 24 seconds

b.) 0.094/6 minutes and 30 seconds

c.) 0.675/6 minutes 30 seconds

d.) 1.29/6 minutes 27 seconds

Answer 1

Arrival rate, ? = 12 per hour

Service rate, ? = 10 per hour (6 minutes per customer, 60/6)

Number of servers (staff accountants) , s = 3

Utilization , p = ?/ s? ?= 12 / 30 = 0.40

Probability that there are no customers = See equation in image

= [ (12/10)^0 / 0! + (12/10)^1 / 1! + (12/10)^2 / 2! + ( (12/10)^3 / 3! * (1/1-0.4))]^-1

=3.64 ^-1 = 0.2941 OR 29.41% of time no customers are there.

Avg. number of students waiting in line = Lq = See equation in image

=[ (0.2941* (12/10) ^3 * 0.4) ] / 3! * (1-0.4)^2 = 0.94118

Waiting time in Queue = Lq / ? = 0.941 / 12 = 0.008 hours = 0.008 * 3600 = ~29 seconds

Total time in system = Waiting time + Service time = 6 minutes + 29 seconds = ~ 6 minutes and 30 seconds

So answer is B