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class+March22 - Math 103 Section 11 Tuesday The Mathematics...

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Math 103, Section 11, Tuesday, March 22, 2011 The Mathematics of Sharing Assignment Chapter 3A Please do Exercises 12,18,30, and 32, pages 105-109 and upload to Sakai. Homework is due by Friday, March 11, 5 minutes before midnight Assignment Chapter 3B Please do Exercises 42, 56, and 70, pages 112-117. Homework is due by Friday, March 25, 5 minutes before midnight Homework to be discussed in class. Page 114, Problem 53 Sealed bids To be discussed in class homework: Page 117, Problem 69 Method of Markers Assignment Chapter 10A Please do Exercises 18, 24, 30, and 36, pages 392-393 and upload to Sakai. Homework to be discussed in class on Friday, March 25 Exercises 1,3,17, 23. Lone-chooser example: Jared, Karla, and Lori are dividing the 18 inch long sub which has a 12 inch vegetarian piece and a 6 inch meat piece The sub is shown in the above picture. The three friends are dividing the sub using the lone-chooser method. Jared likes the vegetarian and meatball parts equally well. Karla is a strict vegetarian and does not eat meat at all, and Lori likes the meatball part twice as much as she likes the vegetarian part. Value table

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Vegetarian Meatball Karla 1 point 0 points Jared 1 point 1 point Lori 1 point 2 points Karla and Jared are the dividers and Lori is the chooser. In the first division, Karla divides the sub into two shares (a left share s1 and a right share s2) and Jared picks the share he likes better. Part a. Describe s1 and s2 using the ruler under the sandwich and using interval notation. For example, [0,1] is interval notation. Put your answers in the table below. Then complete the table . Fill in the following table: Shares s1=[0,6] s2=[6,18] value (% or fraction) to Karla 50% 50% Value (% or fraction) to Jared 6/18=1/3 12/18=2/3 b. Which share does Jared pick? s1 or s2? s2 Why ? Larger value c. Describe how Jared would then subdivide his share into three pieces. Use interval notation. [6,10] [10,14] [14,18] d. Describe how Karla would then subdivide her share into three pieces. Use interval notation. [0,2] [2,4] [4,6] e. Describe the final fair division of the sub and give the value of each player’s share (as a fraction of the total value of the sub in the eyes of the player receiving it) by filling in the following table: Player Shares received at end Value as a fraction Jared [6,10] and [10,14] which is [6,14] 8/18=4/9 Karla [0,2] and [2,4] which is [0,4] 4/12=1/3 Lori [14,18] and [4,6] 10/24=5/12 To Lori the whole sandwich is worth 1*12+2*6=24 points [14,18] is worth 8 points [4,6] is worth 2 points. Here is a clarification of the Method of Sealed Bids. This method involves a money and item exchange among the players. We do not buy items from a store. We already have the items. The highest bidder gets the item. We are careful when we bid.
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This note was uploaded on 01/20/2012 for the course MATH 103 taught by Professor Berkowitz during the Spring '07 term at Rutgers.

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class+March22 - Math 103 Section 11 Tuesday The Mathematics...

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