Question

# ASAPP youre managing an accountant firm during tax season and customers arrive at the rate of...

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

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

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