Problem $1(10$ marks$).$ Al Rashed Goodyear decided to hire a new mechanic to handle all tire changes

for customers ordering a new set of tires. Two mechanics applied for the job. One mechanic has

limited experience, can be hired for $$14$ per hour, and can service an average of three customers per

hour. The other mechanic has several years of experience, can service an average of four customers per

hour, but must be paid $$20$ per hour. Assume that customers arrive at the Goodyear garage at the rate

of two customers per hour. Also, assume Poisson arrivals and exponential service times.

Find the probability that each mechanic is idle.

What is the average number of customers waiting in line for each mechanic?

Limited experience mechanic:

Experienced mechanic:

What is the average amount of time a customer spends in the Goodyear garage?

Limited experience mechanic:

Experienced mechanic:

On the average, how many customers per hour will be served by each mechanic?

Limited experience mechanic:

Experienced mechanic:

If the company assigns a customer waiting cost of $$30$ per hour, which mechanic provides the lower

operating cost?

Limited experience mechanic:

Experienced mechanic: