Math 103:18 Post-class assignment 9 due Apr 22, 2021 1. Eve, Fred, Gail, and Hank are four siblings who inherit a large piece of land. The land is not uniform, and has different features in different...

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Math 103:18 Post-class assignment 9due Apr 22, 2021 1. Eve, Fred, Gail, and Hank are four siblings who inherit a large piece of land. The land is not uniform, and has different features in different locations. A Divider is selected at random, and divides the land into 4 parts (“shares”), which we will call s1, s2, s3, and s4. (a) Eve, Fred, Gail, and Hank each write their assessments of the value of each share, recorded in the following table. For each player, find his/her minimum fair share amount in dollars, find his/her bid list (list of which shares will be fair shares for him/her), and record these in the table: value of s1 value of s2 value of s3 value of s4 Minimum fair share amount in dollars Bid list Eve $240,000 $120,000 $100,000 $140,000 Fred $350,000 $250,000 $150,000 $250,000 Gail $400,000 $100,000 $100,000 $120,000 Hank $250,000 $250,000 $250,000 $250,000 (b) Who must have been the Divider, and how can you tell? (c) There is a "standoff" here between Eve and Gail. Suppose that before the standoff is resolved, Fred is given s4 and Hank is given s3. Describe in words, as specifically as possible in light of the information available, what is done at this stage to resolve the standoff. (d) There is not enough information given to find the exact dollar value of the share which Gail will ultimately receive, after the standoff is resolved. Based on the available information, Gail will receive a share worth at least how much? Is this a fair share, in relation to the original problem of dividing the land among the four siblings? 2. Kelly and Lauren use the Divider-Chooser method to divide use of a retail space over the course of a year. As before Each runs a different type of business. Their individual preferences are as follows: Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec total Kelly 2 1 2 1 3 1 1 1 1 1 1 1 16 Lauren 1 2 2 2 2 3 1 1 1 1 1 1 18 (a) If Lauren is the Divider, at what point in the year does she make the division.? (b) If we call the two shares into which Lauren has divided the year s1 and s2, how much are each of s1 and s2 worth to Kelly, as a fraction (or percentage) of what the whole year is worth? (c) Describe Kelly's share (i.e. which share does she select) and Lauren's share (which share is she left with) at the end of the Divider-Chooser method. Now Jason appears, with documents proving that he too has the rights to a fair share of the retail space. Rather than start over, they agree to use the Lone Chooser method, and build on what Kelly and Lauren have already done. This means that Jason is the Chooser, and Lauren is the first Divider (and she has already done the work of the first division). Here are all their preferences: Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec total Jason 1 1 1 1 1 1 1 1 1 1 1 1 12 Kelly 2 1 2 1 3 1 1 1 1 1 1 1 16 Lauren 1 2 2 2 2 3 1 1 1 1 1 1 18 Subdivision: (d) Describe the second division which Kelly makes, i.e. describe (in terms of specific months or parts of months) the 3 subshares k1, k2, k3 she creates from her share, and indicate how much each subshare is worth to her. You may describe the value to Kelly in terms of “Kelly points”, or as a fraction of the value of the whole year. (e) Describe the second division which Lauren makes, i.e. describe (in terms of specific months or parts of months) the 3 subshares l1, l2, l3 she creates from her share, and indicate how much each subshare is worth to her. You may describe the value to Lauren in terms of “Lauren points”, or as a fraction of the value of the whole year. Selection: Now Jason, the Chooser, returns. (f) In the following table, write down how much each subshare of Kelly's is worth to Jason, and how much each subshare of Lauren's is worth to Jason. You may describe the value to Jason in terms of “Jason points”, or as a fraction of the value of the whole year. Subshare k1 k2 k3 l1 l2 l3 value to Jason (g) Which subshares does Jason select? (h) By filling out the following table, describe the final fair division of the year (indicating which months each player receives), and find the value of each player’s final share as a fraction (or percentage) of the value of the entire year: Player Subshares received Description (which months or parts of months) Fraction of value of the entire year Jason Kelly Lauren 3. Recall the scenario of problem 1 above, in which Eve, Fred, Gail, and Hank are four siblings who inherit a large piece of land, and use the Lone Divider method to produce a fair division. Suppose that Fred takes a second look at the numbers he originally wrote down, and decides to reevaluate the shares, so that the following is the full set of information before the division is carried out: Value of s1 Value of s2 Value of s3 Value of s4 Eve $240,000 $120,000 $100,000 $140,000 Fred $550,000 $150,000 $150,000 $150,000 Gail $400,000 $100,000 $100,000 $120,000 Hank $250,000 $250,000 $250,000 $250,000 (a) There is a standoff here among Eve, Fred, and Gail. Suppose that before the standoff is resolved, Hank is given s4. Describe in words, as specifically as possible in light of the information available, what is done at this stage to resolve the standoff. [Hint: there’s very little you can say specifically!] (b) There is not enough information given to find the exact dollar value of the share which Gail will ultimately receive, after the standoff is resolved. Based on the available information, Gail will receive a share worth at least how much? Is this a fair share for her, in relation to the original problem of dividing the land among the four siblings? Math 103:18 Post-class assignment 9due Apr 22, 2021 1. Eve, Fred, Gail, and Hank are four siblings who inherit a large piece of land. The land is not uniform, and has different features in different locations. A Divider is selected at random, and divides the land into 4 parts (“shares”), which we will call s1, s2, s3, and s4. (a) Eve, Fred, Gail, and Hank each write their assessments of the value of each share, recorded in the following table. For each player, find his/her minimum fair share amount in dollars, find his/her bid list (list of which shares will be fair shares for him/her), and record these in the table: value of s1 value of s2 value of s3 value of s4 Minimum fair share amount in dollars Bid list Eve $240,000 $120,000 $100,000 $140,000 Fred $350,000 $250,000 $150,000 $250,000 Gail $400,000 $100,000 $100,000 $120,000 Hank $250,000 $250,000 $250,000 $250,000 (b) Who must have been the Divider, and how can you tell? (c) There is a "standoff" here between Eve and Gail. Suppose that before the standoff is resolved, Fred is given s4 and Hank is given s3. Describe in words, as specifically as possible in light of the information available, what is done at this stage to resolve the standoff. (d) There is not enough information given to find the exact dollar value of the share which Gail will ultimately receive, after the standoff is resolved. Based on the available information, Gail will receive a share worth at least how much? Is this a fair share, in relation to the original problem of dividing the land among the four siblings? 2. Kelly and Lauren use the Divider-Chooser method to divide use of a retail space over the course of a year. As before Each runs a different type of business. Their individual preferences are as follows: Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec total Kelly 2 1 2 1 3 1 1 1 1 1 1 1 16 Lauren 1 2 2 2 2 3 1 1 1 1 1 1 18 (a) If Lauren is the Divider, at what point in the year does she make the division.? (b) If we call the two shares into which Lauren has divided the year s1 and s2, how much are each of s1 and s2 worth to Kelly, as a fraction (or percentage) of what the whole year is worth? (c) Describe Kelly's share (i.e. which share does she select) and Lauren's share (which share is she left with) at the end of the Divider-Chooser method. Now Jason appears, with documents proving that he too has the rights to a fair share of the retail space. Rather than start over, they agree to use the Lone Chooser method, and build on what Kelly and Lauren have already done. This means that Jason is the Chooser, and Lauren is the first Divider (and she has already done the work of the first division). Here are all their preferences: Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec total Jason 1 1 1 1 1 1 1 1 1 1 1 1 12 Kelly 2 1 2 1 3 1 1 1 1 1 1 1 16 Lauren 1 2 2 2 2 3 1 1 1 1 1 1 18 Subdivision: (d) Describe the second division which Kelly makes, i.e. describe (in terms of specific months or parts of months) the 3 subshares k1, k2, k3 she creates from her share, and indicate how much each subshare is worth to her. You may describe the value to Kelly in terms of “Kelly points”, or as a fraction of the value of the whole year. (e) Describe the second division which Lauren makes, i.e. describe (in terms of specific months or parts of months) the 3 subshares l1, l2, l3 she creates from her share, and indicate how much each subshare is
Answered Same DayApr 21, 2021

Answer To: Math 103:18 Post-class assignment 9 due Apr 22, 2021 1. Eve, Fred, Gail, and Hank are four siblings...

Preeta answered on Apr 22 2021
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Math 103:18 Post-class assignment 9        due Apr 22, 2021        
1. Eve, Fred, Gail, and Hank are four siblings who inherit a large piece of land. The land is not uniform, and has different features in different locations. A Divider is selected at random, and divides the land into 4 parts (“shares”),
which we will call s1, s2, s3, and s4.
(a) Eve, Fred, Gail, and Hank each write their assessments of the value of each share, recorded in the following table. For each player, find his/her minimum fair share amount in dollars, find his/her bid list (list of which shares will be fair shares for him/her), and record these in the table:
    
    value of s1
    value of s2
    value of s3
    value of s4
    Minimum fair share amount in dollars
    Bid list
    Eve
    $240,000
    $120,000
    $100,000
    $140,000
    [($240,000 + $120,000 + $100,000 + $140,000)/4] = $150,000
    S1 (Since only the worth of this share of land matches expectation of Eve)
    Fred
    $350,000
    $250,000
    $150,000
    $250,000
    $250,000
    S1, S2, S4
    Gail
    $400,000
    $100,000
    $100,000
    $120,000
    $180,000
    S1
    Hank
    $250,000
    $250,000
    $250,000
    $250,000
    $250,000
    S1, S2, S3, S4
(b) Who must have been the Divider, and how can you tell?
Ans: As per Lone Divider method, it is the obligation of the divider to divide the goods into shares of equal value. This theory holds true for divider as per fair distribution methods as well as for fair division. As seen in the table above, Hank valued all the four parts equally and so he should be the divider.
(c) There is a "standoff" here between Eve and Gail. Suppose that before the standoff is resolved, Fred is given s4 and Hank is given s3. Describe in words, as specifically as possible in light of the information available, what is done at this stage to resolve the standoff.
Ans: After S4 is given to Fred and S3 is given to Hank, the plot of land left are S1 and S2. Now if there is a standoff between Eve and Gail, then as per divider-chooser method, two plots S1 and S2 can be consolidated into a single plot, say S and can be divided equally among Eve and Gail.
(d) There is not enough information given to find the exact dollar value of the share which Gail will ultimately receive, after the standoff is resolved. Based on the available information, Gail will receive a share worth at least how much? Is this a fair share, in relation to the original problem of dividing the land among the four siblings?
Ans: The consolidated value of S1 and S2 to Gail was ($400,000 + $100,000) = $500,000. The divider-chooser method at least guarantees half of the consolidated land, worth $250,000. Any plot of land worth at least $250,000 is a fair share for Gail. So as per divider-chooser method, in relation to the original problem of dividing the land among the four siblings, Gail will receive a fair share.
2. Kelly and Lauren use the Divider-Chooser method to divide use of a retail space over the course of a year. ...
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