Reference no: EM131004181

1. A workcenter is used to make two products: A and B. Product A needs a setup time of 10 minutes, and a run time of 2 minutes per unit. Product B needs a setup time of 20 minutes and a run time of 1 minute per unit. If A and B are made alternatingly in batches of 50, what is the average output in an eight hour day? (Include the fractional run that may be necessary towards the end of the day). If the batch sizes were 10, what is the average output in an eight hour day? What is the percentage reduction in output?

2. A proposed new product has these estimates:

Development costs: $1 million each in years 1 and 2

Marketing costs: $50,000 in year 2, and $20,000 in years 3 through 10.

Production cost: $20 per unit in years 3 through 10

Selling price: $50 per unit in years 3 through 6, and $40 per unit in years 7 through 10

Salvage price: $400,000 in year 10

The product will be discontinued in year 10.

Assuming the same sales each year, and a 15% annual rate of return, what sales volume (per year) is needed to break even (in the sense of having a zero NPV)? You can assume that all cash flows occur at the end of each year, and you may use Excel - no printouts are needed.

3. A firm makes mountain bikes and road bikes. Mountain bikes sell for $350, and road bikes sell for $250. At least 200 of each should be made every day. Mountain bikes need 3 labor hours in the fabrication center, and 2 labor hours in the assembly; road bikes need 2 labor hours in the fabrication center and 2 labor hours in the assembly. Each bike also needs half an hour at the testing center. Each day, labor hours available at the fabrication center, assembly, and testing center, are 4000, 3000, and 1000 respectively. Assuming that all bikes made can be sold, how many of each should be made each day to maximize the revenue?

Show the problem formulation clearly, and write the solution (you may use Solver, but no printouts are needed).

4. 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?

5. 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)

6. 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).