Problem $15-11($Algorithmic$)$

Agan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of $3\mathrm{.}2$ 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.

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.

Lq $=$ fill in the blank $1$

L $=$ fill in the blank $2$

Wq $=$ fill in the blank $3$

hours

W $=$ fill in the blank $4$

hours

Pw $=$ fill in the blank $5$

Service goals dictate that an arriving customer should not wait for service more than an average of $8$ minutes. Is this goal being met? If not, what action do you recommend?

If the consultant can reduce the average time spent per customer to $9$ minutes, what is the mean service rate? If required, round your answer to one decimal place.

fill in the blank $7$

customer per hour

Will the service goal be met?