1. Mr. Smith has an income of $50,000. His calculations show that he owes $4,200 in taxes. He could hire a CPA for $400 to review the taxes. There is a 20% chance that the CPA could reduce taxes to $2,500, a 50% chance that taxes are reduced to $3,600, and 30% chance that there is no reduction. Should the CPA be hired? What is the expected gain/loss in hiring the CPA?
2. When three dice are rolled, what is the average value of the maximum number obtained? Find the solution through simulation. (Use at least 100 iterations)
3. At the bank teller's window, arrivals and service times are randomly distributed (inter-arrival times and service times have exponential distributions). There is only one teller at the window. If the arrival rate is ‘x' customers per hour, and the service rate is 15 customers per hour, what is the average waiting time for a customer in the system, including waiting in line and being served, for values of x = 2, 4, 6, 8, 10, 12, 14, 14.5, and 14.8? Also, what is the average utilization of the teller for each of those arrival rates? Give the answer in a table. (It is a single channel, single server, single phase, unlimited waiting space model - the M/M/1 model).