Math 181 Homework 1: Solutions and Additional Problems - Prof. Bruce A. Reznick, Assignments of Mathematics

Download Math 181 Homework 1: Solutions and Additional Problems - Prof. Bruce A. Reznick and more Assignments Mathematics in PDF only on Docsity! Math 181 Homework 1 Due Fri., Sept. 5, 2008 Remember that it’s okay to work in groups, but the answers should be in your own words. Calculators may be helpful; versions of these problems on the exams won’t need them. Use complete sentences, staples or paper clips. No late homework accepted. 0. From the textbook: p.497 – 3, 9, 11, 13, 15. These are odd problems and the answers are in the back. For this reason, I will not grade these problems, but they are still part of what you’re expected to do, and I will write out solutions for them. 1. From the textbook: p.497 – 2. 2. p.497 – 4. 3. p.498 – 8. 4. p.498 – 12. 5. p.499 – 14. 6. p.499 – 16. 7. – This problem uses your number N . Xavier, Yetta and Zoë are the three inheritors of an estate consisting of a house, a painting and a rare stamp collection. In thousands of dollars, they assign the following values to (house, paintings, stamps): X – (N, 246, 211), Y – (225, N, 310), Z – (306, 292, N). Using the Knaster Inheritance Procedure, determine the fair division of the estate. Calculate the percentage of the perceived value of the estate obtained by each inheritor. 8. – Using the data from Bob’s ranking and Carol’s ranking, on p.483, work the allocation of goods from the divorce as an “adjusted winner” problem, with the following translation: Best = 40 points, Second best = 30, Third Best = 20, Worst = 10. 9. – Using the same data set as in the last problem., work the allocation of goods from the divorce as a “Knaster inheritance” problem, with the following table translating preference to a bid: Best = $40,000, Second best = $30,000, Third Best = $20,000, Worst = $10,000.