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 (with the exception of the first project, which is an individual 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 3

(This project must be worked individually)

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.

Project 2, Chapter 4

Part I (10 points)

Solve the following matrix equations for X if possible. If it can't be solved, write "not possible". Assume capital letters represent matrices.

Part II - The Abilene Network (10 points)

Abilene is a nationwide, high speed, Internet Protocol (IP), research and education network created by collaboration among Qwest®, Cisco®, Nortel Networks®, Indiana University and Internet2®. Abilene runs on over 10,000 miles of the Qwest nationwide Synchronous Optical Network (SONET) backbone, and Qwest provides facilities and engineering support for the Abilene Internet Protocol (IP) infrastructure. The contributions of Qwest and these dedicated Corporate Partners have resulted in the creation and successful operation of a backbone network with an estimated value of approximately $500 million.

The predominant Internet2 backbone network, Abilene, is utilized by leading universities in almost all fifty states, including Alaska and Hawaii. Nearly 200 U.S. universities take advantage of Abilene to collaborate on such diverse advanced applications as tele-immersion, virtual laboratories, distance learning, distributed performing arts, tele-medicine and digital libraries.

There is a map of the Abilene network at http://www.qwest.com/about/qwest/internet2/map.html.

I have created a blank incidence matrix that you may wish to print an use to make this easier for you. It requires Adobe Acrobat Reader to view.

When I write "hop" or "network segment", I mean a trip between two cities.

Project 3, Chapter 6

Part I - Probabilities (10 points)

Find the probabilities of the following winning poker hands. Assume aces are high and that five cards are drawn from a standard 52 card deck. Show work and the probabilities.

Part II - Decision Theory (10 points)

John and Mitchy run a computer store. They can purchase 10 computers from Zol and Denny for $1400 each, 30 computers from McGuinn and McGuire for $1300 each, or 50 computers from Sebastian for $1250 each (they can buy from more than one dealer, but only one order per dealer). John and Mitchy sell the computers for $1500 each. Each computer that is left at the end of the month will be sold in a clearance sale for $900. John and Mitchy estimate a loss of goodwill of $50 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.

Project 4, Chapter 8

Part I (10 points)

Consider the following two-person zero-sum game.

  Cereal Dairy Meat Snacks
Baking -3 1 -5 4
Fruits 2 -1 -2 3
Pasta -1 1 3 -2
Soda 3 4 -1 2

The row player is "Rick's Ready Mart" and the column player is "Corissa's Country Market".

Rick and Corissa own the only two grocery stores in town so that a sale for Rick is a loss for Corissa and vice versa. Each week, they each run a special on exactly one type of food in an effort to draw business into their store. The matrix showing the choices and the gain in sales for Rick's store are shown.

Answer the following questions.

Part II (10 points)

Project 5, Chapter 9

Part I - Peg Moving (10 points)

Peg boardA game is played by placing a peg into one of ten holes arranged as shown in the figure. The peg is then randomly moved to one of the adjacent holes (as an example, F is adjacent to C, E, I, and J) until one of the vertices (A, G, or J) is reached.

Part II - Craps (10 points)

Consider the dice game of craps as an absorbing Markov chain. The rules of craps are as follow: A pair of dice are rolled. If the sum on the first roll is a 7 or an 11, you win immediately and the game is over. If the sum on the first roll is a 2, 3, or 12, you lose immediately and the game is over. If the sum on the first roll is a 4, 5, 6, 8, 9, or 10, that sum becomes the "point" and you continue rolling the dice until you roll your point again and win or you roll a 7 and lose.

A worksheet that can be completed is available in PDF format.