Problem $6-10($Algo$)$

A call center employs $1,128$ agents. Every month $47$ employees leave the company and $47$ new employees are hired.

a$.$ How long, on average, does an agent work for this call center?

Suppose the cost of hiring and training a new agent is $$940.$ The manager of this call center believes that increasing agents$$ salaries would keep them working longer at the company. The manager wants to increase the average time that an agent works for the call center to $48$ months, or four years.

b$-1.$ Given the current average working time for agents at this call center, determine the current annual cost for hiring and training.

b$-2.$ Assuming the average time that an agent works for the call center is increased to $48$ months, determine the new annual cost for hiring and training.

b$-3.$ If the time an agent works for the call center is increased to $48$ months on average, how much could the company save on hiring and training costs over a year?