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 $2$pms$.$ 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. Use the table below.$\backslash$table$[[m,lq$

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$)$ What is the average time a customer spends in the system in minutes? Show your

work!

e$)(6$ points$)$ What is the average total number of customers at the call center either waiting or

talking to call agent? Show your work!

f$)(6$ points$)$ 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!