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Unformatted text preview: Math 103: Section 11 April 12, 2011 Review for Exam #2 which includes Chapters 3, 10, and 5 You should review the following topics. Chapter 3 Continuous fair division games: Fair shares Methods are the dividerchooser method, the lonedivider method and the lonechooser method Discrete fair division games: Methods are the method of sealed bids and the method of markers Questions for Review: 1. Is it better to be a divider or a chooser? Why? 2. Suppose that 3 players are using the lonedivider method to divide a pie. A standoff occurs. What does this mean and how is it resolved? 3. 3 people want to use the method of sealed bids to divide a piano and a car. Is this possible? If yes, how can this be done? 4. With the method of sealed bids, how is it possible to get more than your fair share? 5. With the method of markers, each person makes a bid. Will each person get a segment of his bid? Is it possible to get more than your bid? Review problems for Chapter 3 Exercises 1518 dividerchooser 31 &32 lonedivider method 41 & 42 lonechooser method Exercises 69 &70 Method of Markers Problems: Study homework, Takehome quiz for Chapter 3, Notes 1. Alice, Bob, and Carol are dividing 6 items using the method of sealed bids. Their bids on each of the items are given in the following table. Please complete this table. Alice Bob Carol Watch $1 $200 $100 Camera $890 $500 $2500 Clock $5 $2000 $1000 Sunglasses $0 $75 $55 Jacket $50 $50 $450 jet ski $1 $1000 $3000 Total bids Fair share Value of items received Prelim Cash settlement Share of surplus Items received and final cash settlement Solution: 1. Alice, Bob, and Carol are dividing 6 items using the method of sealed bids. Their bids on each of the items are given in the following table. Please complete this table. Alice Bob Carol Watch $1 $200 $100 Camera $890 $500 $2500 Clock $5 $2000 $1000 Sunglasses $0 $75 $55 Jacket $50 $50 $450 jet ski $1 $1000 $3000 Total bids $947 $ 3825 $ 7105 Fair share $316 $ 1275 $ 2368 Value of items received $ 2275 $ 5950 Prelim Cash settlement gets $316 pays  $1000 pays  $3582 Share of surplus $ 1422 $1 422 $1 422 Items received and final cash No items 316+1422=1738 Gets watch, clock, sunglasses Gets camera, jacket, jet ski settlement Gets $17381000+1422=422 Gets $422.3582+1422=2160 Pays $2160. Computation of surplus: Have 316 and 10003582=4582 3164582= 4266 So the surplus is 4266. This is split in 3 ways. So each player’s share of the surplus is 4266/3=1422 Chapter 10 Make sure you know how to use your calculator to solve interest problems. 1. Percentage increase and percentage decrease 2. Simple interest –you should know how to use the formula: F=P+Prt or F=P(1+rt) Where F=the future value of P dollars for t years at an APR of R%....
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 Spring '07
 Berkowitz
 Math, Division, Alice, carol

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