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Unformatted text preview: Math 103, Section 11, Tuesday, March 8, 2011 Chapter 3 Handout 4 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 Tuesday, March 8, 5 minutes before midnight Assignment Chapter 3B Please do Exercises 42, 56, and 70, pages 112-117. Homework is due by Tuesday, March 15, 5 minutes before midnight Try the sealed bid applet on-line. Start at Sakai. Click on Publisher Resources on the left side of the page. Then answer Yes to: Do you want to display the nonsecure items? Then you have access to lots of information. Specifically, try clicking on chapter 3, then click on Applets on the left, and then Sealed Bids. You can experiment with different sealed bids interactively and get a good feel for it. Have fun! Homework to be discussed in class. Page 114, Problem 53 Sealed bids Page 117, Problem 69 Method of Markers Can you predict under what circumstances there will be no surplus in the method of sealed bids? Homework to be discussed in class on Tuesday, March 8. Exercise 4. Jared and Karla bought the half meatball-half vegetarian foot-long sub for $8.00 They plan to divide the sandwich fairly using the divider-chooser method. Jared likes meatball subs two times as much as vegetarian subs. Karla likes the vegetarian and meatball parts equally. They just met and don’t know what foods the other likes. Cuts are made perpendicular to the length of the sandwich. [0,6] describes the vegetarian half. [6,8] describes one- third of the meatball half. They flip a coin and Jared is the divider. a. Describe how Jared should cut the sandwich into two shares s1 and s2. b. After Jared cuts, Karla gets to choose. Specify which of the 2 shares Karla should choose and give the value of the share to Karla. Table with values to Jared and Karla. Solution: Let 1 point =value to Jared of 1 inch of vegetarian sub. The 2 points=value to Jared of 1 inch of meatball sub. Whole sandwich has value equal to 1*6+2*6=18 points. Half the sandwich=9 points. Where is the 9 point cut? The 6 inches of veggie is 6 points. Need 3 more points. 1inch of meat=2 points. 1.5 in of meat=3 points. So the cut is at 6+1.5=7.5 inches from the left of the sandwich. That is, 6 inches of veggie and 1.5 inches of meat. Answer to Exercise 4. s1=[ 0,7.5 ] s2=[7.5,12 ] Jared 50% or $4.00 50% or $4.00 Karla 7.5/12=62.5% or $5. 4.5/12=37.5%or $3. Another solution using good old fashioned algebra! Let x=value of 1 inch of vegetarian sub to Jared. Then 2x=value of 1 inch of meatball sub to Jared. Whole sandwich has value=6x+6*2x=$8 18x=$8. Or x=$8/18=$4/9=$.44 That is, 1 inch of veggie sub=44 cents to Jared. 1 inch of meatball sub=88 cents to Jared....
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- Spring '07