Mathematical Applications for the Management, Life, and Social Sciences
12th Edition
ISBN: 9781337625340
Author: Ronald J. Harshbarger, James J. Reynolds
Publisher: Cengage Learning
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Chapter 3.1, Problem 9E
To determine
The element
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7. [10 marks]
Let G
=
(V,E) be a 3-connected graph. We prove that for every x, y, z Є V, there is a
cycle in G on which x, y, and z all lie.
(a) First prove that there are two internally disjoint xy-paths Po and P₁.
(b) If z is on either Po or P₁, then combining Po and P₁ produces a cycle on which
x, y, and z all lie. So assume that z is not on Po and not on P₁. Now prove that
there are three paths Qo, Q1, and Q2 such that:
⚫each Qi starts at z;
• each Qi ends at a vertex w; that is on Po or on P₁, where wo, w₁, and w₂ are
distinct;
the paths Qo, Q1, Q2 are disjoint from each other (except at the start vertex
2) and are disjoint from the paths Po and P₁ (except at the end vertices wo,
W1, and w₂).
(c) Use paths Po, P₁, Qo, Q1, and Q2 to prove that there is a cycle on which x, y, and
z all lie. (To do this, notice that two of the w; must be on the same Pj.)
Chapter 3 Solutions
Mathematical Applications for the Management, Life, and Social Sciences
Ch. 3.1 - (a) Do matrices A and B have the same...Ch. 3.1 -
Ch. 3.1 - 3. (a) What matrix D must be added to matrix A...Ch. 3.1 - Prob. 4CPCh. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Prob. 4ECh. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...
Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Prob. 9ECh. 3.1 - Prob. 10ECh. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Prob. 21ECh. 3.1 - Prob. 22ECh. 3.1 - Prob. 23ECh. 3.1 - In Problems 15-28, perform the operations if...Ch. 3.1 - Prob. 25ECh. 3.1 - In Problems 15-28, perform the operations if...Ch. 3.1 - Prob. 27ECh. 3.1 - Prob. 28ECh. 3.1 - Prob. 29ECh. 3.1 - Prob. 30ECh. 3.1 - In Problems , find and.
Ch. 3.1 - In Problems , find and.
Ch. 3.1 - Prob. 33ECh. 3.1 - 34. Find and if
Ch. 3.1 - 35. Endangered species The tables below give the...Ch. 3.1 - 36. Asian demographics The following tables show...Ch. 3.1 - Prob. 37ECh. 3.1 - Prob. 38ECh. 3.1 - 39. Sales Let matrix A represent the sales (in...Ch. 3.1 - 40. Opinion polls A poll of people revealed...Ch. 3.1 - Prob. 41ECh. 3.1 - 42. National health expenditures The following...Ch. 3.1 - Prob. 43ECh. 3.1 - 44. Debt payment Ace, Baker, and Champ are being...Ch. 3.1 - Prob. 45ECh. 3.1 - Prob. 46ECh. 3.1 - 47. Management Management is attempting to...Ch. 3.1 -
48. Ranking To rank the five members of a...Ch. 3.1 - 49. Production and inventories Operating from two...Ch. 3.1 - Prob. 50ECh. 3.1 - 51. Management In an evaluation of labor...Ch. 3.1 - Prob. 52ECh. 3.1 - 53. For the data in the Problem , use an Excel...Ch. 3.1 - 54. For the data in problem, use an Excel...Ch. 3.2 - What is element if with and
Ch. 3.2 - 2. Find the product.
and
Ch. 3.2 - 3. (a) Compute if and
(b) Can the product...Ch. 3.2 - In Problems 1-4, multiply the matrices.
Ch. 3.2 - In Problems 1-4, multiply the matrices.
Ch. 3.2 - In Problems 1-4, multiply the matrices.
Ch. 3.2 - In Problems 1-4, multiply the matrices.
Ch. 3.2 - In Problems 5-24, use matrices through. In...Ch. 3.2 - In Problems 5-24, use matrices through. In...Ch. 3.2 - In Problems 5-24, use matrices through. In...Ch. 3.2 - Prob. 8ECh. 3.2 - Prob. 9ECh. 3.2 - Prob. 10ECh. 3.2 - Prob. 11ECh. 3.2 - In Problems 5-24, use matrices through. In...Ch. 3.2 - In Problems 5-24, use matrices through. In...Ch. 3.2 - Prob. 14ECh. 3.2 - In Problems 5-24, use matrices through. In...Ch. 3.2 - Prob. 16ECh. 3.2 - Prob. 17ECh. 3.2 - Prob. 18ECh. 3.2 - Prob. 19ECh. 3.2 - Prob. 20ECh. 3.2 - Prob. 21ECh. 3.2 - Prob. 22ECh. 3.2 - In Problems 5-24, use matrices through. In...Ch. 3.2 - Prob. 24ECh. 3.2 - In Problems 25-34, use the matrices below....Ch. 3.2 - Prob. 26ECh. 3.2 - Prob. 27ECh. 3.2 - Prob. 28ECh. 3.2 - Prob. 29ECh. 3.2 - Prob. 30ECh. 3.2 - Prob. 31ECh. 3.2 - Prob. 32ECh. 3.2 - Prob. 33ECh. 3.2 - Prob. 34ECh. 3.2 - Prob. 35ECh. 3.2 - Prob. 36ECh. 3.2 - Prob. 37ECh. 3.2 - 38. For
Are and defined?
What size is each...Ch. 3.2 - Prob. 39ECh. 3.2 - In each of Problems , substitute the given values...Ch. 3.2 - Prob. 41ECh. 3.2 - Prob. 42ECh. 3.2 - Prob. 43ECh. 3.2 - Prob. 44ECh. 3.2 - 45. Car pricing A car dealer can buy midsize cars...Ch. 3.2 - . Revenue A clothing manufacturer has factories...Ch. 3.2 - Prob. 47ECh. 3.2 - . Area and population Matrix below gives the...Ch. 3.2 - 49. Population dynamics Suppose that for a...Ch. 3.2 - 50. Nutrition Suppose the weights (in grams) and...Ch. 3.2 - Prob. 51ECh. 3.2 - Encoding messages Multiplication by a matrix can...Ch. 3.2 - Oil refineries When gasoline is refined from...Ch. 3.2 - 54. Production A manufacturer of small kitchen...Ch. 3.2 - 55. Accounting The annual budget of the Magnum...Ch. 3.2 - 56. Accounting Consider the original budget...Ch. 3.3 - CHECKPOINT
(a) Write the augmented matrix for...Ch. 3.3 - Prob. 2CPCh. 3.3 - CHECKPOINT
For each system of equations, the...Ch. 3.3 - CHECKPOINT
For each system of equations, the...Ch. 3.3 - Prob. 5CPCh. 3.3 - In a problem 1 and 2 use the indicated row...Ch. 3.3 -
In problem 1 and 2, use the indicated row...Ch. 3.3 - In problem 3 and 4, write the augmented matrix...Ch. 3.3 - In problem 3 and 4, write the augmented matrix...Ch. 3.3 -
In problem 5-10, an augmented matrix for a...Ch. 3.3 - Prob. 6ECh. 3.3 - In problem 5-10, an augmented matrix for a system...Ch. 3.3 - In problem 5-10, an augmented matrix for a system...Ch. 3.3 - In problem 5-10, an augmented matrix for a system...Ch. 3.3 - Prob. 10ECh. 3.3 -
In problem 11-16, use row operations on...Ch. 3.3 -
In problem 11-16, use row operations on...Ch. 3.3 - In problem 11-16, use row operations on augmented...Ch. 3.3 -
In problem 11-16, use row operations on augmented...Ch. 3.3 - Prob. 15ECh. 3.3 - Prob. 16ECh. 3.3 -
In problem 17- 20, a system of linear equations...Ch. 3.3 -
In problem 17- 20, a system of linear equations...Ch. 3.3 - In problem 17- 20, a system of linear equations...Ch. 3.3 -
In problem 17- 20, a system of linear equations...Ch. 3.3 - Prob. 21ECh. 3.3 - Prob. 22ECh. 3.3 - Prob. 23ECh. 3.3 - In systems of equations in problem 23 – 36 may...Ch. 3.3 - Prob. 25ECh. 3.3 - Prob. 26ECh. 3.3 - Prob. 27ECh. 3.3 -
In systems of equations in problem 23 – 36 may...Ch. 3.3 - Prob. 29ECh. 3.3 - In systems of equations in problem 23 – 36 may...Ch. 3.3 - Prob. 31ECh. 3.3 - In systems of equations in problem 23 – 36 may...Ch. 3.3 - Prob. 33ECh. 3.3 - Prob. 34ECh. 3.3 - Prob. 35ECh. 3.3 - Prob. 36ECh. 3.3 - Prob. 37ECh. 3.3 - Prob. 38ECh. 3.3 - Prob. 39ECh. 3.3 - Prob. 40ECh. 3.3 - Prob. 41ECh. 3.3 - Prob. 42ECh. 3.3 - Prob. 43ECh. 3.3 - Prob. 44ECh. 3.3 - 45. Nutrition A preschool has Campbell’s Chunky...Ch. 3.3 -
46. Ticket sales A 3500-seat theatre sells...Ch. 3.3 -
47. Investment A man has $235,000 invested in...Ch. 3.3 -
48. Loans A bank lent $1.2 million for the...Ch. 3.3 -
49. Car rental patterns A car rental agency in...Ch. 3.3 -
50. Nutrition A psychologist studying the...Ch. 3.3 - 51. Nutrition The following table gives the...Ch. 3.3 -
52. Investment A brokerage house offers three...Ch. 3.3 -
53. Investment Suppose that portfolios I and II...Ch. 3.3 - 54. Nutrition Each ounce of substance A supplies...Ch. 3.3 - 55. Nutrition A glass of skim milk supplies 0.1 mg...Ch. 3.3 -
56. Transportation The King Trucking Company has...Ch. 3.3 - Nutrition A botanist can purchase plant food of...Ch. 3.3 - Traffic flow In the analyst of traffic flow, a...Ch. 3.3 - Nutrition Three different bacteria are cultured in...Ch. 3.3 - Irrigation An irrigation system allows water to...Ch. 3.3 - Investment An investment club has set a goal to...Ch. 3.3 - A trust account client has to be invested. The...Ch. 3.3 - 63. Investment A brokerage house offers three...Ch. 3.4 - [Type here]
CHECKPOINT
Are the matricesand...Ch. 3.4 - Prob. 2CPCh. 3.4 - Prob. 3CPCh. 3.4 - [Type text]
If is a matrix and is its inverse,...Ch. 3.4 - Prob. 2ECh. 3.4 - Prob. 3ECh. 3.4 - Prob. 4ECh. 3.4 - [Type text]
In Problems 5-10, find the inverse...Ch. 3.4 - [Type text]
In Problems 5-10, find the inverse...Ch. 3.4 - Prob. 7ECh. 3.4 - Prob. 8ECh. 3.4 - Prob. 9ECh. 3.4 - Prob. 10ECh. 3.4 - Prob. 11ECh. 3.4 - Prob. 12ECh. 3.4 - Prob. 13ECh. 3.4 - Prob. 14ECh. 3.4 - [Type here]
In Problems 15-20, find the inverse...Ch. 3.4 - Prob. 16ECh. 3.4 - Prob. 17ECh. 3.4 - [Type here]
In Problems 15-20, find the inverse...Ch. 3.4 - Prob. 19ECh. 3.4 - Prob. 20ECh. 3.4 - Prob. 21ECh. 3.4 - Prob. 22ECh. 3.4 - [Type here]
In Problems 23-26, the inverse of...Ch. 3.4 - [Type here]
In Problems 23-26, the inverse of...Ch. 3.4 - [Type here]
In Problems 23-26, the inverse of...Ch. 3.4 - [Type here]
In Problems 23-26, the inverse of...Ch. 3.4 - Prob. 27ECh. 3.4 - [Type here]
28. Use the inverse found in Problem...Ch. 3.4 - Prob. 29ECh. 3.4 - Prob. 30ECh. 3.4 - [Type here]
In Problems 29-32, use inverse...Ch. 3.4 - [Type here]
In Problems 29-32, use inverse...Ch. 3.4 - Prob. 33ECh. 3.4 - Prob. 34ECh. 3.4 - Prob. 35ECh. 3.4 - Prob. 36ECh. 3.4 - Prob. 37ECh. 3.4 - Prob. 38ECh. 3.4 - Prob. 39ECh. 3.4 - Prob. 40ECh. 3.4 - Prob. 41ECh. 3.4 - Prob. 42ECh. 3.4 - Prob. 43ECh. 3.4 - Prob. 44ECh. 3.4 - Prob. 45ECh. 3.4 - Prob. 46ECh. 3.4 - Prob. 47ECh. 3.4 - Prob. 48ECh. 3.4 - Prob. 49ECh. 3.4 - Prob. 50ECh. 3.4 - 51. Competition A product is made by only two...Ch. 3.4 -
52. Demographics Suppose that a government study...Ch. 3.4 -
In Problems 53-63, set up each system of...Ch. 3.4 -
In Problems 53-63, set up each system of...Ch. 3.4 -
In Problems, set up each system of equations and...Ch. 3.4 -
In problems , set up each system of equations...Ch. 3.4 - In Problems 5363, set up each system of equations...Ch. 3.4 - In Problems 5363, set up each system of equations...Ch. 3.4 - In Problems set up each system of equations and...Ch. 3.4 - In Problems set up each system of equations and...Ch. 3.4 - In Problems 53-63, set up each system of equations...Ch. 3.4 - In Problems set up each system of equations and...Ch. 3.5 - CHECKPOINT
The following technology matrix for a...Ch. 3.5 - Prob. 2CPCh. 3.5 - CHECKPOINT
3. Suppose a primitive economy has wood...Ch. 3.5 - Prob. 4CPCh. 3.5 - The following technology matrix for a simple...Ch. 3.5 - For the economy in Problem 1, what industry is...Ch. 3.5 - Prob. 3ECh. 3.5 - Prob. 4ECh. 3.5 - The following technology matrix describes the...Ch. 3.5 - The following technology matrix describes the...Ch. 3.5 - Prob. 7ECh. 3.5 - Prob. 8ECh. 3.5 - Prob. 9ECh. 3.5 - Prob. 10ECh. 3.5 - Suppose a primitive economy consists of two...Ch. 3.5 - Suppose an economy has two industries, agriculture...Ch. 3.5 - Prob. 13ECh. 3.5 - Prob. 14ECh. 3.5 - Suppose the economy of an underdeveloped country...Ch. 3.5 - Suppose a simple economy with only an agricultural...Ch. 3.5 - Prob. 17ECh. 3.5 - An underdeveloped country has an agricultural...Ch. 3.5 - A simple economy has an electronic components...Ch. 3.5 - Prob. 20ECh. 3.5 - A primitive economy consists of a fishing industry...Ch. 3.5 - An economy has a manufacturing industry and a...Ch. 3.5 - Prob. 23ECh. 3.5 - Prob. 24ECh. 3.5 - Prob. 25ECh. 3.5 - Interdepartmental costs Within a company is a...Ch. 3.5 - Suppose that an economy has three industries...Ch. 3.5 - Prob. 28ECh. 3.5 - Suppose that the economy of a small nation has an...Ch. 3.5 - Suppose an economy has the same technology matrix...Ch. 3.5 - Suppose that a simple economy has three...Ch. 3.5 - Prob. 32ECh. 3.5 - Problems 33-38 refer to closed Leontief models....Ch. 3.5 - Problems 33-38 refer to closed Leontief models....Ch. 3.5 - Problems 33-38 refer to closed Leontief models....Ch. 3.5 - Problems 33-38 refer to closed Leontief models....Ch. 3.5 - Problems 33-38 refer to closed Leontief models....Ch. 3.5 - Problems 33-38 refer to closed Leontief models.
A...Ch. 3.5 - Prob. 39ECh. 3.5 - Card tables are made by joining legs and a top...Ch. 3.5 - Prob. 41ECh. 3.5 - A log carrier has a body made from a -ft length of...Ch. 3 - Use the matrices below a needed to complete...Ch. 3 - Use the matrices below a needed to complete...Ch. 3 - Prob. 3RECh. 3 - Prob. 4RECh. 3 - Prob. 5RECh. 3 - Prob. 6RECh. 3 - Prob. 7RECh. 3 - Prob. 8RECh. 3 - Prob. 9RECh. 3 - Prob. 10RECh. 3 - Prob. 11RECh. 3 - Prob. 12RECh. 3 - Prob. 13RECh. 3 - Prob. 14RECh. 3 - Prob. 15RECh. 3 - Prob. 16RECh. 3 - Prob. 17RECh. 3 - Prob. 18RECh. 3 - Prob. 19RECh. 3 - Prob. 20RECh. 3 - Prob. 21RECh. 3 - Prob. 22RECh. 3 - Prob. 23RECh. 3 - Prob. 24RECh. 3 - Prob. 25RECh. 3 - Prob. 26RECh. 3 - Prob. 27RECh. 3 - Prob. 28RECh. 3 - Prob. 29RECh. 3 - Prob. 30RECh. 3 - In Problems 30-36, solve each system using...Ch. 3 - Prob. 32RECh. 3 - In Problems 30-36, solve each system using...Ch. 3 - Prob. 34RECh. 3 - Prob. 35RECh. 3 - Prob. 36RECh. 3 - Prob. 37RECh. 3 - Prob. 38RECh. 3 - Prob. 39RECh. 3 - Prob. 40RECh. 3 - Prob. 41RECh. 3 - Prob. 42RECh. 3 - Prob. 43RECh. 3 - Prob. 44RECh. 3 - Prob. 45RECh. 3 - Prob. 46RECh. 3 - Prob. 47RECh. 3 - Prob. 48RECh. 3 - The Burr Cabinet Company manufactures bookcases...Ch. 3 - Prob. 50RECh. 3 - A small church choir is made up of men and women...Ch. 3 - Manufacturing Two departments of a firm, and ,...Ch. 3 - Prob. 53RECh. 3 - Investment A woman has to invest. She has decided...Ch. 3 - Nutrition A biologist is growing three different...Ch. 3 - Transportation An airline company has three types...Ch. 3 - Economy models An economy has a shipping industry...Ch. 3 - Economy models A simple economy has a shoe...Ch. 3 - Economy models A look at the industrial sector of...Ch. 3 - Economy models Suppose a closed Leontief model for...Ch. 3 - Prob. 1TCh. 3 - Prob. 2TCh. 3 - Prob. 3TCh. 3 - Prob. 4TCh. 3 - Prob. 5TCh. 3 - Prob. 6TCh. 3 - Prob. 7TCh. 3 - Prob. 8TCh. 3 - Prob. 9TCh. 3 - Prob. 10TCh. 3 - Prob. 11TCh. 3 - Prob. 12TCh. 3 - Prob. 13TCh. 3 - Prob. 14TCh. 3 - Suppose that the solution of an investment problem...Ch. 3 - Prob. 16TCh. 3 - Prob. 17TCh. 3 - Prob. 18TCh. 3 - Prob. 19TCh. 3 - Prob. 20TCh. 3 -
21. Suppose the technology matrix for a closed...Ch. 3 -
Use the following information in Problem ...Ch. 3 -
Use the following information in Problem ...Ch. 3 - Prob. 24TCh. 3 - Prob. 1EAGP1Ch. 3 - Prob. 2EAGP1Ch. 3 - Prob. 3EAGP1Ch. 3 - Prob. 4EAGP1Ch. 3 - Prob. 5EAGP1Ch. 3 - Prob. 6EAGP1Ch. 3 - Prob. 7EAGP1Ch. 3 - Prob. 1EAGP2Ch. 3 - Prob. 2EAGP2Ch. 3 - Prob. 3EAGP2Ch. 3 - Prob. 4EAGP2
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