Problem $3.(39$ points$)$ Managing and Estimating Delays. AUzon$$s customer call center wants you to

analyze its operation for the time between $1$pm and $2$pm$.$ On average, it takes $15$ minutes to handle a

call with a standard deviation of $12$ minutes. Calls come in every $2$ minutes on average with a standard

deviation of $2\mathrm{.}5$ minutes during this period. DO NOT use the Queuing Models and the Excel spreadsheet

to answer the questions below. Instead, use the table below to answer the questions.

a$)(5$ points$)$ What is the capacity of each call agent call center in calls per hour? Show your work!

b$)(5$ points$)$ What is the minimum number of call agents to strictly handle the demand? Show your

work!

c$)(3$ points$)$ What is the capacity of the call center, if $9$ agents are scheduled to answer calls, in

calls per hour? Show your work!

d$)(6$ points$)$ If $9$ agents are scheduled to answer calls, what is the average time a customer spends

in the system in minutes? Show your work!

e$)(6$ points$)$ If $9$ agents are scheduled to answer calls, what is the average total number of

customers at the call center either waiting or talking to call agent? Show your work!

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f$)(6$ points$)$ If $9$ agents are scheduled to answer calls, what is the percentage of time $($probability$)$

that the customer call center is idle? Show your work!

g$)(8$ points$)$ At most, how many call agents should be scheduled for this period to keep the

utilization of the call center at least at $70\%?$ Show your work!

NOTE: SHOW ALL YOUR WORK $->$ UNSUBSTANTIATED ANSWERS RECEIVE NO CREDIT. USE $4$ DECIMAL

PLACES IN ALL CALCULATIONS.

SUBMISSION REQUIREMENTS: UPLOAD ONE FILE TO CANVAS IN PDF$.$ IF YOU WORK ON A PIECE OF

PAPER, THEN YOU CAN TAKE A PHOTO OF THE PAGES, AND CREATE A SINGLE $$PDF$$ FILE AND THEN