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

$($a$)$ Compute the operating characteristics of the customer waiting line, assuming Poisson arrivals and exponential service times. $($Round your answers to four

decimal places. Report time in hours.$)$

$,=,$

$,=,$

$L_q,=,$

$L,$

$W_q,=,h$

$W,=,h$

$P_w,=,$

$($b$)$ Service goals dictate that an arriving customer should not wait for service more than an average of $5$ minutes. Is this goal being met? $($Round your

answer to one decimal place.$)$

$W_q(in$ minutes$)=,$ min, which $is|,$ than the desired wait time, $so$ the goal $----$Select$---$ met.

What action do you recommend? $($Select all that apply.$)$

Increase the mean service rate.

Hire another consultant.

Increase the hours of operation.

There is no need to change the current operating parameters.

Decrease the mean service rate.

$($c$)$ If the consultant can reduce the average time spent per customer to $7$ minutes, what is the mean service rate? $($Round your answers to four decimal

places. Report time in hours.$)$

$=$

$L_q=$

$w_q=$

h

Will the service goal be met? $($Round your answer to one decimal place.$)$

$W_q(in$ minutes$)=--------$ min