Agan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of $2\mathrm{.}6$ 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.$)$

$=$

$=$

$L_q=$

$L=$

$W_q=$

$W=$

$P_w=$

$$

$$

$$

$$

$$ h

$$

$$

$($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$)=$

$$ min, which is $-$Select$-$than the desired wait time, so the goal $$ met.

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

Decrease the mean service rate.

Hire another consultant.

Increase the hours of operation.

There is no need to change the current operating parameters.

Increase 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.$)$

$=$

$L_q=$

$w_q=$

$$

$$