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Math 103:18 Post-class assignment 10due 11pm Apr 29, 2021 1. Larry, Curly, and Mo dissolve their business partnership and must carry 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 computer company car Larry $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 computer company car value of minimum fair share Larry $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) Carry 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 Larry Curly Mo (c) Find the surplus after the first settlement is over, and how much of the surplus each player receives. (d) Carry 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 Larry 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 briefly. 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 arranged 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 arrangement 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 10due 11pm Apr 29, 2021 1. Larry, Curly, and Mo dissolve their business partnership and must carry 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 computer company car Larry $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 computer company car value of minimum fair share Larry $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) Carry 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 Larry Curly Mo (c) Find the surplus after the first settlement is over, and how much of the surplus each player receives. (d) Carry 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 Larry 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 briefly. 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 arranged 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 arrangement 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.