Problem

$2$

$($

$5$

$$marks

$)$

$.$

$$Yasmin Interiors 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 consuitant averages

$1$

$0$

$$minutes with each customer. Assume Poisson arrivals and exponential service times.

$2$

$.$

$$Service goals dictate that an arriving customer should not wait for service more than an average of

$5$

$$minutes$.$ Is this goal being met? If not, what action do you recommend?

$3$

$.$

$$What service rate would be required so that customers average only

$5$

$$minutes in the queue?

$4$

$.$

$$The management at Yasmin Interiors would like to evaluate two alternatives:

Use one consultant with an average service time of

$5$

$$minutes per customer.

Expand to two consultants, each of whom has an average service time of

$1$

$0$

$$minutes per customer.

If the consultants are paid $

$1$

$6$

$$per hour and the customer waiting time is valued at $

$2$

$5$

$$per hour for waiting time prior to service, should Yasmin Interiors expand to the two

$-$

consultant system?