Math 103, Spring 2011, Solutions to Chapter 1 homework
25 total points constitute a perfect score
Problem 12: 6 points
The plurality method requires us to examine first place votes, and only first place votes.
A receives
B receives
C receives
D receives
3
Math 103, Fall 2016
Solutions to homework on Fair Division
Fair Division HW1. Four siblings, Wendy, Xavier, Yolanda, and Zachary, inherit a house.
Suppose that
Wendy considers the house to be worth $400,000
Xavier considers it worth $450,000
Yolanda consi
1.Read Section 3.7 The Method of Markers
Homework to be discussed in class.
2. Can you predict under what circumstances there will be no surplus
in the method of sealed bids? Please e-mail the answer to me or tell
me in class.
We will discuss this in clas
Math 103, Spring 2015
Solutions for Fair Distribution Assignment 2
HW4. 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
placem
Assignment 4
(Covering material from 4.1 4.5 + ME1)
1. The Placerville General Hospital has a nursing staff of 225 nurses working in four shifts A
(7am to 1 pm), B (1pm to 7pm), C (7pm to 1am), and D (1am to 7am). The number of nurses
apportioned to each
Math 103, Spring 2013, Homework for chapter 4: Mathematics of Apportionment
1. (Based on chapter 4 problem #4 in the textbook) The Placerville General Hospital has a
nursing staff of 225 nurses working in four shifts:
A (7am 1pm)
B (1pm 7pm)
C (7pm 1am)
D
Math 103
Exam #2
April 19, 2011
Name_
There are 11 problems and 2 extra credit problem.
Good luck and have fun! Show me all youve learned !
1. 10 points
Alex, Judy, and Lois are dividing the 18 inch long sub which has a 12 inch vegetarian
piece and a 6 in
Math 103, Spring 2011, Solutions to Chapter 3A homework
Problem 12:
The given table is completed by using the fact that each partner values the entire piece of land at
$400,000. This implies that each row (not column!) must add up to $400,000:
Adams
Benso
Math 103 Section 11
Chapter 4 Quiz
Name_
February 25, 2011
10 points
1. A small city operates four bus routes which it calls W, X, Y, and Z, and owns 30 buses. The town decides to
apportion the buses among the four routes based on the average number of pa
Math 103, Spring 2013, homework SOLUTIONS for chapter 3 (Mathematics of Sharing)
1. Martha and Nick share the rights to use a certain store location, but they have separate
businesses, and only one can use the space at a time. To minimize the costs and ha
1
Measuring Power
We turn our attention in this chapter from the candidates to the voters, some of whom may cast more
votes than others, and thereby possess more power than others. This inequality might seem
outrageous to our intuitions at first, but ther
The Mathematics of Sharing
There are 5 problems that we will discuss in class on Tuesday, March 8.
Homework to be discussed in class on Tuesday, March 8.
Problem 1. Divider-chooser problem:
Supp 3.1. Martha and Nick share the rights to use a certain store
Math 103
Exam #2-Solutions
April 19, 2011
There are 11 problems and 2 extra credit problem.
Good luck and have fun! Show me all youve learned !
1. 10 points
Alex, Judy, and Lois are dividing the 18 inch long sub which has a 12 inch vegetarian
piece and a
Homework 1B
(covering material from 1.3-1.5)
The following question, and most of the questions for this chapter, pertains to an election which
is held to select the president of an organization. The candidates are Ann (A), Bob (B), Claire
(C), and Dave (D
Assignment 3A
(Covering material from 3.1 3.4)
[Warmup problems in the book: #15, 17]
1. Martha and Nick share the rights to use a certain store location, but they have separate busi nesses, and only one can use the space at a time. To minimize the costs
Math 103: Section 11
12, 2011
April
Review for Exam #2 which includes Chapters 3, 10, and 5
You should review the following topics.
Chapter 3
Continuous fair division games: Fair shares
Methods are the divider-chooser method, the lone-divider method and t
Math 103 Spring 2013, homework for chapter 1
Please remember to use complete English sentences when writing your solutions.
See the document How to submit assignments in Sakai in the Resources folder of your Math
103 sections Sakai site.
1. The following
Math 103, Section 11
Exam #1
March 4, 2011
Name_
Please show me all youve learned in the course so far! I know youll do very well!
Please show your work. There are 9 problems and 2 extra credit problems.
Formulas: 1+2+3+L= L (L+1)
2
Formulas: 1+2+3+N-1= (
Assignment 3B
(Covering material from 3.3, 3.5, 3.7)
1. Ann, Bob, and Chris have equal claims to a store location, and are using the Lone Divider
method to find a fair division of access to the location over the calendar year. We assume as in
problem 1 th
Math 103, Spring 2013, Homework on Weighted Voting Systems Solutions
1. [Suggested warm-ups from the textbook for this homework problem are #11, 13, 15, and 17]
Consider the weighted voting system [12: 9, 4, 3, 2].
1a. Write out all winning coalitions for
Math 103 Spring 2015, Voting Theory Assignment 2
Please remember to use complete English sentences when writing your solutions.
See the document How to submit assignments in Sakai in the Resources folder of the Sakai site for your
Math 103 section.
HW2. T
Math 103, Spring 2015
Growth and Finance Assignment 1
HW1. Suppose that the US population is growing by 0.96% each year, and continues to grow at
this rate every year.
a. What is the overall growth factor for 40 years of population growth? By what overall
Math 103, Spring 2015, Measuring Power Assignment 1 Solutions
HW1. Consider the weighted voting system [12: 9, 4, 3, 2].
a. Write out all winning coalitions for this weighted voting system, and underline the
critical player(s) in each one.
b. Find the Ban
Math 103, Spring 2015
Growth and Finance Assignment 4
HW10. Suppose that starting when you are 22, you invest $3,000 at the end of each year in an
IRA (individual retirement account) with an APR of 6% compounded annually. Interest is paid
at the end of th
Math 103, Spring 2015
Fair Distribution Assignment 1
HW1. Wendy and Xavier are siblings who have inherited a house from their parents. They are not willing
to share the house (growing up together was enough), so one or the other will receive it when their
Math 103:15/11, Spring 2015
Fair Division Assignment 1
HW1. Martha and Nick share the rights to use a certain store location, but they have separate
businesses, and only one can use the space at a time. To minimize the costs and hassles of
turnover, they
Math 103 Spring 2015, Voting Theory Assignment 2 - Solutions
Please remember to use complete English sentences when writing your solutions.
See the document How to submit assignments in Sakai in the Resources folder of the Sakai site for your
Math 103 sec
Chapters 1,2,4 Review Sheet
Note: This only represents a sampling of questions and does not represent all possible questions. It is strongly
advised that you study all examples in notes, odd numbers from the textbook, and homework as well.
CHAPTER 1
Part
Math 103 Spring 2015, Voting Theory Assignment 1 - Solutions
Please remember to use complete English sentences when writing your solutions.
See the document How to submit assignments in Sakai in the Resources folder of the Sakai site for your
Math 103 sec
Math 103, Fall 2015
Solutions to homework fair distribution
Fair Distribution HW3. Ed, Faith, and Greg must distribute 3 oranges (O), 4 pears (P), and 5 apples (A)
among themselves. Since they are doing this before a trip, they dont wish to slice up indiv
They are not willing to share the house (growing up together was enough), so one or the other will receive
it when their parents estate is settled. This is the only item which they have inherited, and they apply the
Method of Sealed Bids to obtain a fair
Solutions
1. An election is held, in which there are four candidates A, B, C, and D, and the following preference schedule is
obtained:
10
7
4
2
1st place
A
D
B
C
2nd place
B
C
A
B
3rd place
C
B
D
D
4th place
D
A
C
A
(a) How many people voted in this elec
HW2 This problem refers to the Gesundheit Hospital described in problem HW1 above.
Shift
# of patients
Morning
1742
Afternoon
2067
Evening
1220
Late night
371
a. Find the Hamilton apportionment of nurses to shifts based on number of patients in
the hospit
HW2. This problem looks again at the weighted voting system in HW1, which was
[12: 9, 4, 3, 2], and considers the effect of changing the quota but leaving all the weights
unchanged. We will call the 4 players A, B, C, and D, respectively.
a. Find the Banz