Question

Agan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of 2.5 customers arrive each hour. One design consultant is available to answer customer questions and make product recommendations. The consultant averages 10 minutes with each customer. Compute the operating characteristics of the customer waiting line, assuming Poisson arrivals and exponential service times. Round your answers to four decimal places. Do not round intermediate calculations.

Answer 1

the operating characteristics have been solved below

Explanation:

we have an average of 10 minutes per customers

μ = mean service rate = 60/10 = 6 customers in one hr

the average number of customers that are waiting in line

mean arrival λ = 2.5

μ = 6

`Lq = (2.5^(2) )/(6(6-2.5)) \\`

= 6.25/21

= 0.2976

we calculate the average number of customers that are in the system

`L=Lq+(2.5)/(6)`

= 0.2976+0.4167

= 0.7143

we find the average time that a customer spends in waiting

`Wq=(0.2976)/(2.5)`

= 0.1190 hours

when converted to minutes = 0.1190*60 = 7.1424 minutes

`0.1190+(1)/(6)`

=0.2857

probability that arriving customers would wait for the service

= 2.5÷6 = 0.4167