A post office is considering whether to assign one or two postal clerks on-duty to keep open on Sunday, from 9 a.m. to 3 p.m. Customers arrive at a rate of 8 per hour following a Poisson distribution and the service times for a customer is 4 minutes, exponentially distributed. The post office has a single queue for customers waiting for an idle postal clerk for service. Suppose the hourly rate of a postal clerk is $16.25, and it is estimated that a cost of $0.65 for each minute a customer spends waiting for service. ( a ) For the 1-clerk scenario, compute the probability that there are more than four customers in the post office. (b ) For the 2-clerk scenario, compute the probability that no customer is in the post office. (c ) By computing the total relevant cost per day for the two scenarios respectively, should the post office schedule 1 or 2 postal clerks on-duty on Sunday?
A post office is considering whether to assign one or two postal clerks on-duty to keep open on Sunday, from 9 a.m. to 3 p.m. Customers arrive at a rate of 8 per hour following a Poisson distribution and the service times for a customer is 4 minutes, exponentially distributed. The post office has a single queue for customers waiting for an idle postal clerk for service. Suppose the hourly rate of a postal clerk is $16.25, and it is estimated that a cost of $0.65 for each minute a customer spends waiting for service. ( a ) For the 1-clerk scenario, compute the probability that there are more than four customers in the post office. (b ) For the 2-clerk scenario, compute the probability that no customer is in the post office. (c ) By computing the total relevant cost per day for the two scenarios respectively, should the post office schedule 1 or 2 postal clerks on-duty on Sunday?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:A post office is considering whether to assign one or two postal clerks on-duty to keep
open on Sunday, from 9 a.m. to 3 p.m. Customers arrive at a rate of 8 per hour following
a Poisson distribution and the service times for a customer is 4 minutes, exponentially
distributed. The post office has a single queue for customers waiting for an idle postal
clerk for service. Suppose the hourly rate of a postal clerk is $16.25, and it is estimated
that a cost of $0.65 for each minute a customer spends waiting for service.
( a ) For the 1-clerk scenario, compute the probability that there are more than four
customers in the post office.
(b ) For the 2-clerk scenario, compute the probability that no customer is in the post
office.
(c ) By computing the total relevant cost per day for the two scenarios respectively,
should the post office schedule 1 or 2 postal clerks on-duty on Sunday?
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