$(12$ points$)$

The fire department has a number of failures with its oxygen masks and is evaluating the

possibility of outsourcing the preventive maintenance to the manufacturer. Because of the risk

associated with a failure, the cost of each failure is estimated at $$2,000.$ The current maintenance

policy $($with station employees performing maintenance$)$ has yielded the following history:

a$)$ What is the expected annual cost of the current maintenance policy with station employees

performing maintenance?

b$)$ Based on the results from part a$)$ which is the more economical practice to use? Assume that

if the maintenance is outsourced, the workers currently performing this work will keep their jobs.