Problem $15-11($Algorithmic$)$

Agan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of $2\mathrm{.}4$ customers arrive each hour. One design consultant is available to answer customer questions and make product recommendations. The consultant averages $12$ minutes with each customer.

a$.$ Compute the operating characteristics of the customer waiting line, assuming Poisson arrivals and exponential service times. If required, round your answers to four decimal places.

$L_q=$

$L=$

$w_q=$

hours

$w=$

hours

$P_w=$

b$.$ Service goals dictate that an arriving customer should not wait for service more than an average of $4$ minutes. Is this goal being met? If not, what action do you recommend?

c$.$ If the consultant can reduce the average time spent per customer to $8$ minutes, what is the mean service rate? If required, round your answer to one decimal place.

customer per hour

Will the service goal be met?