## Math 160 - Projects

Listed below are the various projects that will be required throughout the semester. Each of these are worth 20 points and will be due the day following the exam for the appropriate chapter. These projects take you above and beyond the material covered in the book or require outside data acquisition. You may work in groups of up to three people per project. Turn in one project with all group member's names on it. Plan on reading the section of the book dealing with the matter before we cover it in class; you will not always have time to finish the project if you wait until we do.

### Project 1, Chapter 4

Part I (10 points)

• Chapter 4 Group Activity, pages 254 - 255 in the textbook. Work Parts A and B.

Part II (10 points)

MCI is one of the major players in the Internet backbone game. A map of the backbone can be found at http://www.mci.com/resources/iguide/framelements/textiguide2.2.shtml

• Create an incidence matrix for the MCI national backbone. List the cities in alphabetical order.
• What is the maximum number of hops a packet might travel before reaching its destination?
• If the site at Washington DC goes down, what is the maximum number of hops a packet might travel before reaching its destination (assume its destination isn't Washington DC)?

### Project 2, Chapter 6

John and Mitchy run a computer store. They can purchase 10 computers from Zol and Denny for \$2000 each, 30 computers from McGuinn and McGuire for \$1800 each, or 50 computers from Sebastian for \$1700 each (they can buy from more than one dealer, but only one order per dealer). John and Mitchy sell the computers for \$2100 each. Each computer that is left at the end of the month will be sold in a clearance sale for \$1300. John and Mitchy estimate a loss of goodwill of \$100 for each customer which comes into the store, but is unable to purchase a computer. During the month, the customers will either demand 15, 30, 45, or 60 computers. Assume the probability of 15, 30, 45, or 60 computers is 0.10, 0.15, 0.50, and 0.25 respectively.

• Create a payoff table with the five actions (purchase plans) and four states of nature (demand)
• Create the opportunistic loss (regret) table.
• For each decision criteria (expected value, maximax, maximin, minimax), find the payoff or loss and the best action.

### Project 3, Chapter 8

• Work the group activity on page 564.

### Project 4, Chapter 9

• Work the group activity on pages 612 - 613.

### Project 5, Chapter 3

Your project is to plan a retirement fund for yourself. To simplify calculations, assume all transactions - starting of annuity fund, retirement, and death - occur on your birthday. Assume a nominal interest rate of 6% has been guaranteed for the remainder of your life.

• Identify the age you will be on your birthday this year.
• Identify the age at which you wish to retire. Identify the number of years before retirement.
• Identify the age at which you anticipate dying. Identify the number of years of retirement.
• Identify the monthly payment you anticipate needing during your retirement.
• Calculate the present value necessary on the date of retirement to finance your retirement.
• The present value needed to retire is the future value necessary upon retirement. Calculate the monthly payment needed before retirement to have enough money to retire.
• Calculate the amount of money in your retirement fund after ten years assuming you make the regular payments just calculated.
• After the ten years, assume that you receive an inheritance of \$20,000 and add it to your retirement fund. If you stop making regular payments, and just let what money is in the account draw interest, what will the amount be at the time of retirement?
• Subtract this amount from the future value needed upon retirement and recompute the monthly payment necessary to obtain the future value. Remember that ten years have gone by. If no more monthly payments are needed, then state the monthly benefit when you retire.