Question $1$ to Question $6$ is based on this problem.

Boot Barn sells cowboy boot and western wear through catalogs and the web. Customers can phone in orders at any time day or night, $7$ days a week. During the $1$ am to $9$ am shift, a single sales rep handles all calls. During this time, calls arrive at a rate of $14$ per hour following a Poisson distribution. It takes the sales rep an average of four minutes to process each call. The variability in service times is approximately exponentially distributed. All calls received while the sales rep is busy are placed in a queue.

Which of the following statement regarding this problem is not true?

Group of answer choices

A$.$

M$/$M$/$s model is suitable to analyze this problem.

B$.$

$\backslash$lambda $=14$

C$.$

$\backslash$mu $=4$

D$.$

M$/$M$/1$ model can be used to analyze the problem.

Flag question: Question $2$

Question $21$ pts

On average, how long must customers wait in line before talking to the sales rep? Rounding decimals of your calculation to units.

Group of answer choices

$56$ minutes

$60$ minutes

$33$ minutes

$72$ minutes

a duration $($in minutes$)$ different from all the above

Flag question: Question $3$

Question $31$ pts

On average, how many people are on hold? Keeping four decimals of your calculation.

Group of answer choices

$13\mathrm{.}0667$

$14\mathrm{.}0000$

$0\mathrm{.}9333$

$14\mathrm{.}9333$

a number different from all the above

Flag question: Question $4$

Question $41$ pts

If one additional rep is hired to work during the $1$ am to $9$ am period, what is the average amount of time a customer spends in the system? Keeping three decimals of your calculation.

Group of answer choices

$1\mathrm{.}116$ minutes

$5\mathrm{.}112$ minutes

$54\mathrm{.}882$ minutes

$6\mathrm{.}228$ minutes

a duration $($in minutes$)$ different from all the above

Flag question: Question $5$

Question $51$ pts

With the additional rep working during the $1$ am to $9$ am$,$ what effect would this have on the average amount of time it takes to serve a customer? Keeping one decimals of your answer if needed.

Group of answer choices

A$.$

The service time is reduced by $0\mathrm{.}1$ minutes.

B$.$

The service time is reduced by $0\mathrm{.}3$ minutes.

C$.$

The service time is reduced by $0\mathrm{.}8$ minutes.

D$.$

The service time is reduced by a positive amount of time different from all the above.

E$.$

No effect

Flag question: Question $6$

Question $61$ pts

Suppose Boot Barn wants there to be no more than a $5\%$ chance that a customer will be placed on hold. How many sales reps should the company employ in total?

Group of answer choices

$1$

$2$

$3$

$4$

$5$

$6$

more than $6$

Flag question: Question $7$

Question $71$ pts

Question $7$ to Question $10$ is based on this problem.

Refer to the previous problem. Suppose that Boot Barn$$s phone system can only keep four calls on hold at any time, the average profit margin of each call is $$55$ and sales reps cost the company $$12$ per hour.

If callers who receive a busy signal take their business elsewhere, how much money is the company losing per hour $($on average$)$ if it employed a single sales rep $($i$.$e$.$ without hiring the additional employee mentioned in previous problem$)?$ Rounding decimals of your calculation to units. Hint: you need to use the arrival rate of customer calls and the probability of balk $($which will be given in the Excel output if you choose the right queue model$)$ in the calculation $.$

Group of answer choices

$$96$

$$107$

$$132$

$$155$

a value different from all the above

Flag question: Question $8$

Question $81$ pts

If callers who receive a busy signal take their business elsewhere, what is the profit the company makes per hour if it employed a single sales rep $($i$.$e$.$ without hiring the additional employee$)?$ Rounding decimals of your calculation to units. Rounding decimals of your calculation to units.

Group of answer choices

$$882$

$$770$

$$651$

$$550$

$$443$

a value different from all the above

Flag question: Question $9$

Question $91$ pts

By how much will the profit increase per hour if the company employs two sales reps instead of one? Rounding decimals of your calculation to units.

Group of answer choices

$$89$

$$96$

$$105$

$$118$

more than $$118$

Flag question: Question $10$

Question $101$ pts

How many sales reps should the company employ if it wants to maximize profit?

Group of answer choices

$1$

$2$

$3$

$4$

$5$

$6$

more than $6$