Part | -Quantitative Analysis [61 points] [33 points} Managing the Pets-Fl-awesDMe lIZaII Center Tim IWoods, a recent EMU MBA grad and serial entrepreneur, has opened PetsR-awesOMe, an online pet store. He and his team are experimenting with call center staffing. a] {13 points] The current call center format has two lines: one for customers who want to place an order and one for customers who want to report a problem. Each line is served by one specialized customer service representative. The call center is staffed so that at any given time, there is one representative taking customer orders and one representative addressing customer problems. On average, there is a new customer who wants to place an order everyr two minutes, exponentially distributed. Similarly; there is a new customer needing to address a problem every two minutes, exponentially distributed. The call center staffers are fast and can on average complete one call of either type in T5 seconds, with a standard deviation of 30 seconds. Each call center staff member is paid $15 per hour. The estimated cost of a customer waiting for a representative is $20 per hour due to lost goodwill and negative word of mouth. Fill in the next table. {Don It forget the units.) Show your work on the table or below. Fill in the next table. (Don't forget the units.) Show your work on the table or below. What type of queuing system is this? Arrival rate Average inter-arrival time Service rate Average service time # of servers Utilization CA2 C$ 2 Avg. # of customers in the line Avg. # of customers in the system Avg. time a customer waits in the line Avg. time a customer waits in the system Probability the system is emptyb) [10 points} One option PetsRawesOMe is considering for its call center is to crosstrain the two staff so thevr can both take orders or solve problems. In this case, all customers [i.e., those wishing to place an order and those wanting to report a problem) will join a single line and will be served by the rst operator available. Each staffer after crosstraining will be paid $15 per hour and will serve customers at the same rate as in parta]. Arrivals are not expected to change for each tvpe of call. The opportunitv cost of waiting for a representative will still be $20 per hour. Should PetsRawesOMe implement this system or keep the existing call center format [part a}?Justifv your answer by calculating the total cost of each option. Please show your work