Project #31189 - Math Applications

Show All work Please

 

 

 

MAT-105: APPLIED LIBERAL ARTS MATHEMATICS

 

Application Assignment 6

The written assignment draws mostly on even-numbered exercises from the textbook. Answer all assigned exercises, and show all work.

 

Each problem is worth 5 points unless a point value is indicated.  Please show work where appropriate for full credit.

 

Section 14.1 Problems 16, 18, 20

 

Use the graph below to answer Exercises 16, 18 & 20

 

 

16.   Which edge(s) shown on the graph are not included in the following path:

       A, B, D, F, E, C ?

 

 

 

18.   On the graph, is it possible to determine a circuit that includes only four distinct vertices?  If so, determine one such circuit.

 

 

 

20.   On the graph, can you determine a circuit that includes all the vertices without using any vertex (other than the beginning and ending vertex) twice?  If so, determine one such circuit.

 

 

 

 

 

 

Section 14.2 Problems 16, 18, 22

 

For Exercises 16 & 18, use the following graph.

 

 

16.   Determine an Euler circuit that begins and ends with vertex B.

 



 

 

18.   Determine an Euler circuit that begins and ends with vertex E.

 

 

 

 

22.   Imagine a very large connected graph that has two odd vertices and 398 even vertices.

 

       a)     Does a Euler path exist for this graph?  Explain.

 

 

 

 

       b)     Does an Euler circuit exist for this graph?  Explain.

 

 

Section 14.3 Problems 24, 26 (10 points for problem 26)

 

24.   A Milk Truck Route.  Dale Klitzke is a milk truck driver for Swiss Valley Farms Cooperative in eastern Iowa.  Dale has to start at the processing plant and pick up milk on 10 different farms.  In how many ways can Dale visit each farm and return to the processing plant?

 

 

 

 

26.   Job Interviews.  Christina Dwyer is searching for a new job.  She lives in Shreveport, Louisiana, and has interviews in Barrow, Alaska; Tucson, Arizona; and Rochester, New York.  The cost of a one-way flights between these four cities are as follows:  Shreveport to Barrow costs $855, Shreveport to Tucson costs $803, Shreveport to Rochester costs$113, Barrow to Tucson costs $393, Barrow to Rochester costs $337, and Tucson to Rochester costs $841.

 

a)Represent this traveling salesman problem with a complete, weighted graph showing the prices of the flights on the appropriate edges.

 

 

 

 

 

 

 

 

b)Use the brute force method to determine the least expensive route for Christina to travel to each city and return home to Shreveport.

 

 




       c)What is the minimum cost she can pay?

 






Section 15.1Problems 14, 16, 18

 

Logo Choice.  In Exercises 14, 16 & 18, employees at the Bloomfield Fire Department are choosing a new department logo.  The choices are a hydrant (H), a fireman (F), and a fire truck (T).  Each employee ranks the three choices from first to third.  The preference table below shows the results of the ballots.

 

 

Number of votes

10

5

4

2

First

H

F

F

T

Second

F

H

T

F

Third

T

T

H

H

 

 

14.   Is there a majority winner?

 

 

 

 

16.   Determine the winner using the Borda count method.

 

 

 

 

18.   Determine the winner using the pairwise comparison method.

 

 

 

 

 

 

Section 15.2 Problems 4, 6, 8, 10

 

In Exercises 4, 6 & 8, fill in the blank with an appropriate word or phrase.

 

4.     If a candidate is the winner of an election and in a second election one or more of the other candidates is removed, the previous winner should still be the winner.  This criterion is called the ________________ method.

 

 

 

6.     A voting method that always satisfies the majority criterion but may not satisfy any other criterion is the ________________ method




8      A voting method that always satisfies the majority criterion and the monotonicity criterion, but may not satisfy any other criterion, is the _______________ method.

 

 

 

 

10.   Reconstructing a Company.  The board of directors at The Limited is considering three different administrative restructuring plans, A, B & C.  The 11 members of the board of directors rank the plans according to the preference table below.

 

Number of votes

2

4

2

3

First

B

A

C

C

Second

A

B

A

B

Third

C

C

B

A

 

 a)     Which restructuring plan is preferred to all others in a head-to-head comparison?

 

 

 

 

  b)     Suppose that the plurality method is used to determine the winner.  Is the head-to-head criterion satisfied?  Explain.

 

 

 

 

 

 

Section 15.3 Problem 8

 

In Exercise 8, fill in the blank with an appropriate word or phrase.

 

8.     a)    The apportionment method that uses a modified divisor that is less than the standard divisor is _________________ method.

 




b)    The apportionment method that uses a modified divisor that is greater than the standard divisor is _________________ method.

 




c)    The apportionment method that uses a modified divisor that could be less than, greater than or equal to the standard divisor is _______________ method.



 

Section 15.4 Problems 4, 6, 8

 

In Exercises 4 & 6, fill in the blank with an appropriate word or phrase.

 

4.     Hamilton's method and Jefferson's method favor ________________ states.

 

 

6.     The apportionment that satisfies the quota rule but may produce a paradox called

 

___________________ method.

 

 

 

8.     Ergonomic Chairs.  A large company with offices in four cities must distribute 148 new ergonomic chairs to the four offices.  The chairs will be apportioned based on the number of employees in each office as shown in the table below.

 

Office

A

B

C

D

Total

Employees

757

295

636

976

2664

 

 

       a)     Apportion the chairs using Hamilton's method.

 

 

 

 

           b)     Does the Alabama paradox occur using Hamilton's method if the number of new chairs is increased from 148 to 149?  Explain your answer.

Subject Mathematics
Due By (Pacific Time) 05/22/2014 12:00 am
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