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.

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 consider the probability of balk. Group of Answers: $$96$; $$107$: $$132$: $$155$; OR a value different from all the above.

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$; OR a value different from all the above

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$

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

Group of answer choice

$1$

$2$

$3$

$4$

$5$

$6$

more than $6$