Discrete Mathematics and Its Applications
8th Edition
ISBN: 9781260501759
Author: ROSEN
Publisher: MCG
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Chapter 11, Problem 15CP
To determine
Use backtracking to color the graph with three colors if adjacency matrix is given.
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Tri-County Utilities, Inc., supplies natural gas to customers in a three-county area. The company purchases natural gas from two companies: Southern Gas and Northwest Gas.
Demand forecasts for the coming winter season are as follows: Hamilton County, 400 units; Butler County, 200 units; and Clermont County, 300 units. Contracts to provide the following quantities have been written: Southern Gas, 500 units; and Northwest Gas, 400 units. Distribution costs for the counties vary, depending upon the location of the suppliers. The distribution costs per unit (in thousands of dollars)
are as follows.
From
To
Hamilton Butler
Clermont
Southern Gas
10
20
15
Northwest Gas
12
15
18
(a) Develop a network representation of this problem. (Submit a file with a maximum size of 1 MB.)
Choose File No file chosen
Assignment 3 graph.docx
Score: 1 out of 1
Comment:
(b) Develop a linear programming model that can be used to determine the plan that will minimize total distribution costs (in thousands of…
Use the method of undetermined coefficients to solve the given nonhomogeneous system.
dx
dt
=
2x + 3y − 8
dy
dt
=
−x − 2y + 6
X(t) =
As discussed in Section 8.3, the Markowitz model uses the variance of the portfolio as the measure of risk. However, variance includes deviations both below and above the mean return. Semivariance includes only deviations below the mean and is considered by many to be a better measure of risk.
(a)
Develop a model that minimizes semivariance for the Hauck Financial data given in the file HauckData with a required return of 10%.
Assume
that the five planning scenarios in the Hauck Financial Services model are equally likely to occur. Hint: Modify model (8.10)–(8.19). Define a variable ds for each scenario and let
ds ≥ R − Rs
with
ds ≥ 0.
Then make the objective function:
Min
1
5
5
s = 1
ds2.
Let
FS = proportion of portfolio invested in the foreign stock mutual fund
IB = proportion of portfolio invested in the intermediate-term bond fund
LG = proportion of portfolio invested in the large-cap growth fund
LV = proportion of portfolio invested in the large-cap value fund…
Chapter 11 Solutions
Discrete Mathematics and Its Applications
Ch. 11.1 - Prob. 1ECh. 11.1 - Vhich of these graphs are trees?Ch. 11.1 - Prob. 3ECh. 11.1 - Prob. 4ECh. 11.1 - Prob. 5ECh. 11.1 - Prob. 6ECh. 11.1 - Prob. 7ECh. 11.1 - Prob. 8ECh. 11.1 - Prob. 9ECh. 11.1 - Prob. 10E
Ch. 11.1 - Prob. 11ECh. 11.1 - Prob. 12ECh. 11.1 - Prob. 13ECh. 11.1 - Prob. 14ECh. 11.1 - Let G he a simple graph with n vertices. Show that...Ch. 11.1 - Prob. 16ECh. 11.1 - Prob. 17ECh. 11.1 - Prob. 18ECh. 11.1 - Prob. 19ECh. 11.1 - Prob. 20ECh. 11.1 - Prob. 21ECh. 11.1 - A chain letter starts when a person sends a letter...Ch. 11.1 - A chain letter starts with a person sending a...Ch. 11.1 - Prob. 24ECh. 11.1 - Prob. 25ECh. 11.1 - Prob. 26ECh. 11.1 - Prob. 27ECh. 11.1 - Prob. 28ECh. 11.1 - Prob. 29ECh. 11.1 - Prob. 30ECh. 11.1 - Prob. 31ECh. 11.1 - Prob. 32ECh. 11.1 - Prob. 33ECh. 11.1 - Prob. 34ECh. 11.1 - Prob. 35ECh. 11.1 - Prob. 36ECh. 11.1 - Letnbe a power of 2. Show thatnnumbers can be...Ch. 11.1 - Prob. 38ECh. 11.1 - Prob. 39ECh. 11.1 - Prob. 40ECh. 11.1 - Prob. 41ECh. 11.1 - Prob. 42ECh. 11.1 - Prob. 43ECh. 11.1 - Prob. 44ECh. 11.1 - Draw the first seven rooted Fibonacci trees.Ch. 11.1 - Prob. 46ECh. 11.1 - Prob. 47ECh. 11.1 - Show that the average depth of a leaf in a binary...Ch. 11.2 - Build a binary search tree for the...Ch. 11.2 - Build a binary search tree for the words oenology,...Ch. 11.2 - How many comparisons are needed to locate or to...Ch. 11.2 - How many comparisons are needed to locate or to...Ch. 11.2 - Using alphabetical order, construct a binary...Ch. 11.2 - How many weighings of a balance scale are needed...Ch. 11.2 - How many weighings of a balance scale are needed...Ch. 11.2 - How many weighings of a balance scale are needed...Ch. 11.2 - How many weighings of a balance scale are needed...Ch. 11.2 - One of four coins may be counterfeit. If it is...Ch. 11.2 - Find the least number of comparisons needed to...Ch. 11.2 - Prob. 12ECh. 11.2 - The tournament sort is a sorting algorithm that...Ch. 11.2 - The tournament sort is a sorting algorithm that...Ch. 11.2 - Prob. 15ECh. 11.2 - Prob. 16ECh. 11.2 - Prob. 17ECh. 11.2 - The tournament sort is a sorting algorithm that...Ch. 11.2 - The tournament sort is a sorting algorithm that...Ch. 11.2 - The tournament sort is a sorting algorithm that...Ch. 11.2 - Prob. 21ECh. 11.2 - The tournament sort is a sorting algorithm that...Ch. 11.2 - Prob. 23ECh. 11.2 - The tournament sort is a sorting algorithm that...Ch. 11.2 - Prob. 25ECh. 11.2 - The tournament sort is a sorting algorithm that...Ch. 11.2 - Prob. 27ECh. 11.2 - Prob. 28ECh. 11.2 - Suppose thatmis a positive integer with m>2An...Ch. 11.2 - Suppose that m is a positive integer with m>2 An...Ch. 11.2 - Suppose that m is a positive integer withm= 2. An...Ch. 11.2 - Suppose thatmis a positive integer withm= 2....Ch. 11.2 - Prob. 33ECh. 11.2 - Prob. 34ECh. 11.2 - Suppose that m is a positive integer with m>2 An...Ch. 11.2 - Prob. 36ECh. 11.2 - Suppose that m is a positive integer with m>2 An...Ch. 11.2 - Suppose that m is a positive integer with m>2 An...Ch. 11.2 - Prob. 39ECh. 11.2 - Suppose that m is a positive integer withm= 2. An...Ch. 11.2 - Prob. 41ECh. 11.2 - Suppose that m is a positive integer with m>2 An...Ch. 11.2 - Prob. 43ECh. 11.2 - Prob. 44ECh. 11.3 - Prob. 1ECh. 11.3 - Prob. 2ECh. 11.3 - Prob. 3ECh. 11.3 - Prob. 4ECh. 11.3 - Suppose that the vertex with the largest address...Ch. 11.3 - Prob. 6ECh. 11.3 - Prob. 7ECh. 11.3 - Prob. 8ECh. 11.3 - Prob. 9ECh. 11.3 - Prob. 10ECh. 11.3 - Prob. 11ECh. 11.3 - Prob. 12ECh. 11.3 - Prob. 13ECh. 11.3 - Prob. 14ECh. 11.3 - Prob. 15ECh. 11.3 - Prob. 16ECh. 11.3 - Prob. 17ECh. 11.3 - a) Represent the compound propositionsandusing...Ch. 11.3 - a) Represent(AB)(A(BA))using an ordered rooted...Ch. 11.3 - In how many ways can the stringbe fully...Ch. 11.3 - In how many ways can the stringbe fully...Ch. 11.3 - Draw the ordered rooted tree corresponding to each...Ch. 11.3 - What is the value of each of these prefix...Ch. 11.3 - What is the value of each of these postfix...Ch. 11.3 - Prob. 25ECh. 11.3 - Prob. 26ECh. 11.3 - Prob. 27ECh. 11.3 - Prob. 28ECh. 11.3 - Prob. 29ECh. 11.3 - Prob. 30ECh. 11.3 - Show that any well-formed formula in prefix...Ch. 11.3 - Prob. 32ECh. 11.3 - Prob. 33ECh. 11.3 - Prob. 34ECh. 11.4 - How many edges must be removed from a connected...Ch. 11.4 - Prob. 2ECh. 11.4 - Prob. 3ECh. 11.4 - Prob. 4ECh. 11.4 - Prob. 5ECh. 11.4 - Prob. 6ECh. 11.4 - Prob. 7ECh. 11.4 - Prob. 8ECh. 11.4 - Prob. 9ECh. 11.4 - Prob. 10ECh. 11.4 - Prob. 11ECh. 11.4 - Prob. 12ECh. 11.4 - Prob. 13ECh. 11.4 - Prob. 14ECh. 11.4 - Prob. 15ECh. 11.4 - Prob. 16ECh. 11.4 - Prob. 17ECh. 11.4 - Prob. 18ECh. 11.4 - Prob. 19ECh. 11.4 - Prob. 20ECh. 11.4 - Prob. 21ECh. 11.4 - Describe the tree produced by breadth-first search...Ch. 11.4 - Prob. 23ECh. 11.4 - Explain how breadth-first search or depth-first...Ch. 11.4 - Prob. 25ECh. 11.4 - Prob. 26ECh. 11.4 - Prob. 27ECh. 11.4 - Use backtracking to find a subset, if it exists,...Ch. 11.4 - Explain how backtracking can be used to find a...Ch. 11.4 - Prob. 30ECh. 11.4 - Prob. 31ECh. 11.4 - A spanning forest of a graphGis a forest that...Ch. 11.4 - Prob. 33ECh. 11.4 - Prob. 34ECh. 11.4 - Prob. 35ECh. 11.4 - A spanning forest of a graphGis a forest that...Ch. 11.4 - Prob. 37ECh. 11.4 - Prob. 38ECh. 11.4 - Prob. 39ECh. 11.4 - Prob. 40ECh. 11.4 - Prob. 41ECh. 11.4 - Prob. 42ECh. 11.4 - Prob. 43ECh. 11.4 - Prob. 44ECh. 11.4 - Prob. 45ECh. 11.4 - Prob. 46ECh. 11.4 - Prob. 47ECh. 11.4 - Prob. 48ECh. 11.4 - Prob. 49ECh. 11.4 - Prob. 50ECh. 11.4 - Prob. 51ECh. 11.4 - Prob. 52ECh. 11.4 - Prob. 53ECh. 11.4 - Prob. 54ECh. 11.4 - Prob. 55ECh. 11.4 - Prob. 56ECh. 11.4 - Prob. 57ECh. 11.4 - Prob. 58ECh. 11.4 - Prob. 59ECh. 11.4 - Prob. 60ECh. 11.4 - Prob. 61ECh. 11.5 - The roads represented by this graph are all...Ch. 11.5 - Prob. 2ECh. 11.5 - Prob. 3ECh. 11.5 - Prob. 4ECh. 11.5 - Prob. 5ECh. 11.5 - Prob. 6ECh. 11.5 - Prob. 7ECh. 11.5 - Prob. 8ECh. 11.5 - Prob. 9ECh. 11.5 - Prob. 10ECh. 11.5 - Prob. 11ECh. 11.5 - Prob. 12ECh. 11.5 - Prob. 13ECh. 11.5 - Prob. 14ECh. 11.5 - Prob. 15ECh. 11.5 - Prob. 16ECh. 11.5 - Prob. 17ECh. 11.5 - Prob. 18ECh. 11.5 - Prob. 19ECh. 11.5 - Prob. 20ECh. 11.5 - Prob. 21ECh. 11.5 - Prob. 22ECh. 11.5 - Express the algorithm devised in Exercise 22 in...Ch. 11.5 - Prob. 24ECh. 11.5 - Prob. 25ECh. 11.5 - Prob. 26ECh. 11.5 - Prob. 27ECh. 11.5 - Prob. 28ECh. 11.5 - Prob. 29ECh. 11.5 - Prob. 30ECh. 11.5 - Prob. 31ECh. 11.5 - Prob. 32ECh. 11.5 - Prob. 33ECh. 11.5 - Prob. 34ECh. 11.5 - Prob. 35ECh. 11 - Prob. 1RQCh. 11 - Prob. 2RQCh. 11 - Prob. 3RQCh. 11 - Prob. 4RQCh. 11 - Prob. 5RQCh. 11 - Prob. 6RQCh. 11 - Prob. 7RQCh. 11 - a) What is a binary search tree? b) Describe an...Ch. 11 - Prob. 9RQCh. 11 - Prob. 10RQCh. 11 - a) Explain how to use preorder, inorder, and...Ch. 11 - Show that the number of comparisons used by a...Ch. 11 - a) Describe the Huffman coding algorithm for...Ch. 11 - Draw the game tree for nim if the starting...Ch. 11 - Prob. 15RQCh. 11 - Prob. 16RQCh. 11 - a) Explain how backtracking can be used to...Ch. 11 - Prob. 18RQCh. 11 - Prob. 19RQCh. 11 - Show that a simple graph is a tree if and Only if...Ch. 11 - Prob. 2SECh. 11 - Prob. 3SECh. 11 - Prob. 4SECh. 11 - Prob. 5SECh. 11 - Prob. 6SECh. 11 - Prob. 7SECh. 11 - Prob. 8SECh. 11 - Prob. 9SECh. 11 - Prob. 10SECh. 11 - Prob. 11SECh. 11 - Prob. 12SECh. 11 - Prob. 13SECh. 11 - Prob. 14SECh. 11 - Prob. 15SECh. 11 - Prob. 16SECh. 11 - Prob. 17SECh. 11 - Prob. 18SECh. 11 - Prob. 19SECh. 11 - Prob. 20SECh. 11 - Prob. 21SECh. 11 - Prob. 22SECh. 11 - Prob. 23SECh. 11 - The listing of the vertices of an ordered rooted...Ch. 11 - The listing of the vertices of an ordered rooted...Ch. 11 - Prob. 26SECh. 11 - Prob. 27SECh. 11 - Prob. 28SECh. 11 - Prob. 29SECh. 11 - Show that if every circuit not passing through any...Ch. 11 - Prob. 31SECh. 11 - Prob. 32SECh. 11 - Prob. 33SECh. 11 - Prob. 34SECh. 11 - Prob. 35SECh. 11 - Prob. 36SECh. 11 - Prob. 37SECh. 11 - Prob. 38SECh. 11 - Prob. 39SECh. 11 - Prob. 40SECh. 11 - Prob. 41SECh. 11 - Prob. 42SECh. 11 - Prob. 43SECh. 11 - Prob. 44SECh. 11 - Prob. 45SECh. 11 - Show that a directed graphG= (V,E) has an...Ch. 11 - In this exercise we will develop an algorithm to...Ch. 11 - Prob. 1CPCh. 11 - Prob. 2CPCh. 11 - Prob. 3CPCh. 11 - Prob. 4CPCh. 11 - Prob. 5CPCh. 11 - Prob. 6CPCh. 11 - Prob. 7CPCh. 11 - Given an arithmetic expression in prefix form,...Ch. 11 - Prob. 9CPCh. 11 - Given the frequency of symbols, use Huffman coding...Ch. 11 - Given an initial position in the game of nim,...Ch. 11 - Prob. 12CPCh. 11 - Prob. 13CPCh. 11 - Prob. 14CPCh. 11 - Prob. 15CPCh. 11 - Prob. 16CPCh. 11 - Prob. 17CPCh. 11 - Prob. 18CPCh. 11 - Prob. 1CAECh. 11 - Prob. 2CAECh. 11 - Prob. 3CAECh. 11 - Prob. 4CAECh. 11 - Prob. 5CAECh. 11 - Prob. 6CAECh. 11 - Prob. 7CAECh. 11 - Prob. 8CAECh. 11 - Prob. 1WPCh. 11 - Prob. 2WPCh. 11 - Prob. 3WPCh. 11 - DefineAVL-trees(sometimes also known...Ch. 11 - Prob. 5WPCh. 11 - Prob. 6WPCh. 11 - Prob. 7WPCh. 11 - Prob. 8WPCh. 11 - Prob. 9WPCh. 11 - Prob. 10WPCh. 11 - Discuss the algorithms used in IP multicasting to...Ch. 11 - Prob. 12WPCh. 11 - Describe an algorithm based on depth-first search...Ch. 11 - Prob. 14WPCh. 11 - Prob. 15WPCh. 11 - Prob. 16WPCh. 11 - Prob. 17WPCh. 11 - Prob. 18WP
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