Math 103:18 Post-class assignment 10 due 11pm Apr 29, 2021
1. La
y, Curly, and Mo dissolve their business partnership and must ca
y out a fair distribution of 5 valuable items which they own jointly. They use the Method of Sealed Bids to make the distribution, and write out their bids as follows:
Painting
office
desk
compute
company ca
La
y
$20,000
$245,000
$4,000
$3,000
$28,000
Curly
$50,000
$300,000
$4,000
$3,000
$30,000
Mo
$27,000
$260,000
$5,000
$4,000
$34,000
(a) Find the value of each player’s minimum fair share, in dollars.
Painting
office
desk
compute
company ca
value of minimum fair share
La
y
$20,000
$245,000
$4,000
$3,000
$28,000
Curly
$50,000
$300,000
$4,000
$3,000
$30,000
Mo
$27,000
$260,000
$5,000
$4,000
$34,000
(b) Ca
y out the allocation of the items, and the first settlement.
First settlement:
Items received (if any), and their value
$ initially paid to bank account
$ initially received from bank account
La
y
Curly
Mo
(c) Find the surplus after the first settlement is over, and how much of the surplus each player receives.
(d) Ca
y out the final settlement (for each player, indicate the items received and net amount of cash paid or received as of the end of the process).
Final settlement:
Items received (if any), and their value
net $ paid to bank account after the surplus is distributed
net $ received from bank account after the surplus is distributed
La
y
Curly
Mo
(e) Suppose that after the first settlement, the banker runs off with all the surplus money. Do the players still end up with fair shares in spite of not receiving the surplus money? Explain
iefly.
2. Ed, Faith, and Greg must distribute 6 oranges (O), 4 pears (P), and 5 apples (A) among themselves. Since they are doing this before a trip, they don’t wish to slice up individual pieces of fruit, but instead wish each piece to go to one person. They decide to use the method of markers, and their individual preferences are as follows:
· Ed likes all types of fruit equally
· Faith likes only Apples and Pears, not Oranges
· Greg likes Oranges twice as much as Pears, and likes Pears and Apples equally
The items are a
anged in the following order. Place each player's markers. You do not need to find which share goes to which player! Placing the markers is all you need to do.
O A O P A A O P A O P P O O A
3. Ann (A), Bob (B), Claire (C), and Dave (D) use the method of markers to divide a collection of 15 albums, labeled by letters L through Z. The a
angement of the albums, and the placement of the players’ markers, is as follows:
B1
A1
C1
B2
A2
C2
A3
C3
B3
D3
D1
D2
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
Which items does each player receive? Which items are leftovers? Explain your reasoning.
Math 103:18 Post-class assignment 10 due 11pm Apr 29, 2021
1. La
y, Curly, and Mo dissolve their business partnership and must ca
y out a fair distribution of 5 valuable items which they own jointly. They use the Method of Sealed Bids to make the distribution, and write out their bids as follows:
Painting
office
desk
compute
company ca
La
y
$20,000
$245,000
$4,000
$3,000
$28,000
Curly
$50,000
$300,000
$4,000
$3,000
$30,000
Mo
$27,000
$260,000
$5,000
$4,000
$34,000
(a) Find the value of each player’s minimum fair share, in dollars.
Painting
office
desk
compute
company ca
value of minimum fair share
La
y
$20,000
$245,000
$4,000
$3,000
$28,000
Curly
$50,000
$300,000
$4,000
$3,000
$30,000
Mo
$27,000
$260,000
$5,000
$4,000
$34,000
(b) Ca
y out the allocation of the items, and the first settlement.
First settlement:
Items received (if any), and their value
$ initially paid to bank account
$ initially received from bank account
La
y
Curly
Mo
(c) Find the surplus after the first settlement is over, and how much of the surplus each player receives.
(d) Ca
y out the final settlement (for each player, indicate the items received and net amount of cash paid or received as of the end of the process).
Final settlement:
Items received (if any), and their value
net $ paid to bank account after the surplus is distributed
net $ received from bank account after the surplus is distributed
La
y
Curly
Mo
(e) Suppose that after the first settlement, the banker runs off with all the surplus money. Do the players still end up with fair shares in spite of not receiving the surplus money? Explain
iefly.
2. Ed, Faith, and Greg must distribute 6 oranges (O), 4 pears (P), and 5 apples (A) among themselves. Since they are doing this before a trip, they don’t wish to slice up individual pieces of fruit, but instead wish each piece to go to one person. They decide to use the method of markers, and their individual preferences are as follows:
· Ed likes all types of fruit equally
· Faith likes only Apples and Pears, not Oranges
· Greg likes Oranges twice as much as Pears, and likes Pears and Apples equally
The items are a
anged in the following order. Place each player's markers. You do not need to find which share goes to which player! Placing the markers is all you need to do.
O A O P A A O P A O P P O O A
3. Ann (A), Bob (B), Claire (C), and Dave (D) use the method of markers to divide a collection of 15 albums, labeled by letters L through Z. The a
angement of the albums, and the placement of the players’ markers, is as follows:
B1
A1
C1
B2
A2
C2
A3
C3
B3
D3
D1
D2
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
Which items does each player receive? Which items are leftovers? Explain your reasoning.