Three brothers have inherited some items. You see their bids on the items in the bid table below. Hal Dan Lou Diamond ring 800 700 550 Gold crown 400 900 700 Silver sword 450 350 550 The brothers decide that Hal will keep the silver sword and will receive $200. Dan will keep the diamond ring and gold crown and will pay $900. Lou will get no items and will receive $700. Use this information to answer questions 1 and 2. Hal Dan Lou Diamond ring 800 700 550 Gold crown 400 900 700 Silver sword 450 350 550 Cash b fs x xb 1. (15 points) Fill out the table above. 2. (2 points) Is this a fair division for everyone? Why or why not? MA 111 Mini-exam 3 - Page 3 of 5 Spring 2023 A group of explorers discovers a gold statue hidden deep in the jungle, and they must arrange a fair division. The table below shows their bids. Use this information to answer questions 3 through 9. Jane Jack Sam Damien Chloe Statue 40 80 50 30 100 3. (2 points) Find each person's fair share of the statue. (Make clear each person's fair share.) 4. (2 points) List which explorers could possibly take the statue and still arrange a fair division using cash payments. For questions 5 and 6, suppose the explorers decide on the following division: Jane, Sam, and Damien receive $10 each Chloe receives $20 Jack gets the statue and pays $70 5. (2 points) Is the division described here a fair division? Why or why not? 6. (2 points) In the division described here, is all the cash accounted for? If not, how much is the surplus? MA 111 Mini-exam 3 - Page 4 of 5 Spring 2023 7. (2 points) For questions 7, 8, 9, suppose instead that Chloe takes the statue and she pays everyone else their fair share. How much does Chloe pay in total? 8. (2 points) What would Chloe's compensation be in the scenario of problem 7? 9. (2 points) If Chloe takes the statue and pays each of the others their fair share, would this result in a fair division? Explain. MA 111 Mini-exam 3 - Page 5 of 5 Spring 2023 Four siblings Frank, Mary, Paul, and Jane, inherited from their musician uncle a violin, a trumpet, and a flute. It was decided that Frank will get the trumpet, Mary will get the flute, Paul will get the violin. In addition, Mary will pay Jane $280 and Paul will pay Jane $20. The bids of the four siblings are in the following table: Frank Mary Paul Jane Violin 360 280 260 348 Trumpet 280 260 272 380 Flute 480 560 388 372 Cash 0 280 20 300 b fs x xb 10. (16 points) Fill out the above table. 11. (2 points) Is this a fair division for all four siblings? Explain your answer.