Please answer the question on the computer. If handwriting is required, please do not use connected characters. Thank you for your understanding and time!

c$.$ What is the average number of customers who are at the checkout desk, either waiting

or currently being served?

d$.$ Now assume for this question only that $10$ percent of the customers do not rent a video

at all and therefore do not have to go through checkout. What is the average time a

customer has to wait in line before getting served by the checkout employee $($i$.$e$.,$ waiting

time in queue$)?$ Assume that the coefficient of variation for the arrival process remains the

same as before.

Hint: Arrival rate becomes $90\%$ of current arrival rate. This means there are only $36$

customer arriving every hours. You need to calculate the interarrival time for this new

arrival rate.

e$.$ As a special service, the store offers free popcorn and sodas for customers waiting in line

at the checkout desk. $($Note: The person who is currently being served is too busy with

paying to eat or drink.$)$ The store owner estimates that every minute of customer waiting

time costs the store $75$ cents because of the consumed food. What is the optimal number

of employees at checkout? Assume an hourly wage rate of $$10$ per hour, and all

customers need to check out $($i$.$e$.,$ disregard part $($d$)).$

Hint: Tradeoff between the cost of hiring employees and that of customer waiting $($food

consumption$).$ Consider a one hour period, the total cost includes customer waiting cost

$($average number of customers in queue, times $75$ cents per customer per minute, times $60$

minutes per hour$)$ and employee wages $($ $$10$ per hour per employee times the number of

employees$).$ Calculate the total cost when you hire $1,2,$ or $3$ employees and choose the one

with the lowest total cost. Please answer the question on the computer. If handwriting is required, please do not use connected characters. Thank you for your understanding and time!

Atlantic Video, a small video rental store in Philadelphia, is open $24$ hours a day, and$-$due to its

proximity to a major business school$-$experiences customers arriving around the clock. A recent

analysis done by the store manager indicates that there are $30$ customers arriving every hour,

with a standard deviation of interarrival times of $2$ minutes. This arrival pattern is consistent and

is independent of the time of day. The checkout is currently operated by one employee, who

needs on average $1$ minutes to check out a customer. The standard deviation of this check$-$out

time is $3$ minutes, primarily as a result of customers taking home different numbers of videos.

a$.$ If you assume that every customer rents at least one video $($i$.$e$.,$ has to go to the checkout$),$

what is the average time a customer has to wait in line before getting served by the

checkout employee $($i$.$e$.,$ waiting time in queue$)?$

b$.$ If there are no customers requiring checkout, the employee is sorting returned videos, of

which there are always plenty waiting to be sorted. How many videos can the employee

sort over an $8-$hour shift $($assume no breaks$)$ if it takes exactly $1\mathrm{.}5$ minutes to sort a single

video? darr

Hint: similar to part $($a$)$ in Question $2$