Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
3rd Edition
ISBN: 9780134689555
Author: Edgar Goodaire, Michael Parmenter
Publisher: PEARSON
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Chapter 14.2, Problem 1E
Answer the following two questions for each of the directed networks shown.
Show that given flow is not maximum by finding a flow-augmenting chain from s to t. What is the slack in your chain.
Find a maximum flow, given its value, and prove that it is maximum by appealing to Theorem 14.2.2
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In Gallup's Annual Consumption Habits Poll, telephone interviews were conducted for a
random sample of 1014 adults aged 18 and over. One of the questions was, "How many
cups of coffee, if any, do you drink on an average day?" The following table shows the
results obtained (Gallup website, August 6, 2012).
Number of Cups
per Day
0
1
2
3
4 or more
Number of
Responses
365
264
193
91
101
Define a random variable x = number of cups of coffee consumed on an average day. Let
x=4 represent four or more cups.
a. Develop a probability distribution for x.
b. Compute the expected value of x.
c. Compute the variance of x.
d. Suppose we are only interested in adults who drink at least one cup of coffee on an
average day. For this group, let y = the number of cups of coffee consumed on an
average day. Compute the expected value of y and compare it to the expected value of x.
Ten major college football bowl games were played in January 2010, with the University
of Alabama beating the University of Texas 37 to 21 to become the national champion
of college football. The results of the 10 bowl games follow (USA Today, January 8, 2010).
Bowl Game
Score
Outback
Gator
Auburn 38 Northwestern 35
Florida State 33 West Virginia 21
Capital One
Penn State 19 LSU 17
Rose
Ohio State 26 Oregon 17
Florida 51 Cincinnati 24
Sugar
Cotton
Alamo
Fiesta
Mississippi State 21 Oklahoma State 7
Texas Tech 41 Michigan State 31
Boise State 17 TCU 10
Orange
Iowa 24 Georgia Tech 14
Championship
Alabama 37 Texas 21
Predicted
Point Margin
Actual
Point Margin
5
3
1
12
3
-2
14
3
9
-4
-3
4
229740706
14
10
10
16
The predicted winning point margin was based on Las Vegas betting odds approximately
one week before the bowl games were played. For example, Auburn was predicted to beat
Northwestern in the Outback Bowl by five points. The actual winning point margin for Au-
burn was three points. A…
Chapter 14 Solutions
Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
Ch. 14.1 - 1. This directed network illustrates a valid -...Ch. 14.1 - Prob. 2TFQCh. 14.1 - Prob. 3TFQCh. 14.1 - Prob. 4TFQCh. 14.1 - Prob. 5TFQCh. 14.1 - Prob. 6TFQCh. 14.1 - Prob. 7TFQCh. 14.1 - Prob. 8TFQCh. 14.1 - Prob. 9TFQCh. 14.1 - Prob. 10TFQ
Ch. 14.1 - Prob. 1ECh. 14.1 - Prob. 2ECh. 14.1 - Prob. 3ECh. 14.1 - Prob. 4ECh. 14.1 - Answer the following questions for each of the...Ch. 14.1 - Prob. 6ECh. 14.1 - Prob. 7ECh. 14.2 - The chain scabt in this network is...Ch. 14.2 - Prob. 2TFQCh. 14.2 - Prob. 3TFQCh. 14.2 - Prob. 4TFQCh. 14.2 - Prob. 5TFQCh. 14.2 - Prob. 6TFQCh. 14.2 - Prob. 7TFQCh. 14.2 - Prob. 8TFQCh. 14.2 - Prob. 9TFQCh. 14.2 - Prob. 10TFQCh. 14.2 - Answer the following two questions for each of the...Ch. 14.2 - 2. Find a maximum flow for each of the networks in...Ch. 14.2 - Prob. 3ECh. 14.2 - Shown are two networks whose arc capacities are...Ch. 14.3 - 1. To solve a maximum flow problem where are...Ch. 14.3 - Prob. 2TFQCh. 14.3 - Prob. 3TFQCh. 14.3 - Prob. 4TFQCh. 14.3 - Prob. 5TFQCh. 14.3 - Prob. 6TFQCh. 14.3 - Prob. 7TFQCh. 14.3 - Prob. 8TFQCh. 14.3 - If T is a tree, there is a unique path between any...Ch. 14.3 - Prob. 10TFQCh. 14.3 - Prob. 1ECh. 14.3 - Prob. 2ECh. 14.3 - 3. Four warehouses, A,B,C and D. with monthly...Ch. 14.3 - 4. Answer Question 3 again, this time assuming...Ch. 14.3 - Prob. 5ECh. 14.3 - Verify Mengers Theorem, Theorem 14.3.1 for the...Ch. 14.3 - Prob. 7ECh. 14.3 - Prob. 8ECh. 14.3 - Prob. 9ECh. 14.3 - Prob. 10ECh. 14.4 - 1. A graph with 35 vertices cannot have a perfect...Ch. 14.4 - 2. The graph has a perfect matching.
Ch. 14.4 - Prob. 3TFQCh. 14.4 - Prob. 4TFQCh. 14.4 - Prob. 5TFQCh. 14.4 - Prob. 6TFQCh. 14.4 - Prob. 7TFQCh. 14.4 - Prob. 8TFQCh. 14.4 - Prob. 9TFQCh. 14.4 - 10. Hall’s marriage Theorem is named after the...Ch. 14.4 - Prob. 1ECh. 14.4 - :Repeat Exercise 1 with reference to the following...Ch. 14.4 - 3. Determine whether the graph has perfect...Ch. 14.4 - 4. Angela, Brenda, Christine, Helen, Margaret,...Ch. 14.4 - Prob. 5ECh. 14.4 - Bruce, Edgar, Eric, Herb, Maurice, Michael,...Ch. 14.4 - Prob. 7ECh. 14.4 - Prob. 8ECh. 14.4 - Suppose v1,v2 are the bipartition sets in a...Ch. 14.4 - Prob. 10ECh. 14.4 - Prob. 11ECh. 14.4 - Prob. 12ECh. 14.4 - Prob. 13ECh. 14.4 - Prob. 14ECh. 14.4 - Prob. 15ECh. 14.4 - Prob. 16ECh. 14 - Prob. 1RECh. 14 - Prob. 2RECh. 14 - Prob. 3RECh. 14 - Prob. 4RECh. 14 - Prob. 5RECh. 14 - 6.For each network, find a maximum flow and...Ch. 14 - 7.(a) Which graph have the property that for any...Ch. 14 - Prob. 8RECh. 14 - Prob. 9RECh. 14 - Prob. 10RECh. 14 - Prob. 11RE
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