A Transition to Advanced Mathematics
8th Edition
ISBN: 9781285463261
Author: Douglas Smith, Maurice Eggen, Richard St. Andre
Publisher: Cengage Learning
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Chapter 2.6, Problem 7E
(a)
To determine
To find: the number of pairs of shoes selected by the person.
(b)
To determine
To find: the number of ways of selecting four cards.
(c)
To determine
To find: the number of ways of selecting
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(c) Describe the distribution plan and show the total distribution cost.
Optimal Solution
Amount
Cost
$ 2000
Southern-Hamilton
200
Southern-Butler
$
Southern-Clermont
300
4500
Northwest-Hamilton
200
$2400
Northwest-Butler
200
$3000
Northwest-Clermont
$
Total Cost
ક
(d) Recent residential and industrial growth in Butler County has the potential for increasing demand by 100 units.
(i) Create an updated distribution plan assuming Southern Gas becomes the preferred supplier.
Distribution Plan with Southern Gas
Amount
Southern-Hamilton
$
Cost
×
Southern-Butler
x
$
Southern-Clermont
300
$ 4500
Northwest-Hamilton
64
x
Northwest-Butler
$
×
Northwest-Clermont 0
$0
Total Cost
$
(ii) Create an updated distribution plan assuming Northwest Gas becomes the preferred supplier.
Distribution Plan with Northwest Gas
Southern-Hamilton
Southern-Butler
0
Southern-Clermont
Northwest-Hamilton
Northwest-Butler
Northwest-Clermont
Total Cost
Amount
×
x
x
+7
$0
Cost
×
$
×
$
×
+4
$
-/+
$
×
×
The distribution system for the Herman Company consists of three plants, two warehouses, and four customers. Plant capacities and shipping costs per unit (in $) from each plant to each warehouse are as follows.
Warehouse
Plant
Capacity
1
2
1
4
7
450
2
8
5
600
3
5
6
380
Customer demand and shipping costs per unit (in $) from each warehouse to each customer are as follows.
Customer
Warehouse
1
2 3
1
6
4
8
2
3
6
7
7
Demand
300 300 300 400
(a) Develop a network representation of this problem. (Submit a file with a maximum size of 1 MB.)
Choose File No file chosen
This answer has not been graded yet.
(b) Formulate a linear programming model of the problem. (Let Plant 1 be node 1, Plant 2 be node 2, Plant 3 be node 3, Warehouse 1 be node 4, Warehouse 2 be node 5, Customer 1 be node 6, Customer 2 be node 7, Customer 3 be node 8, and Customer 4 be node 9. Express your answers in the form x;;, where x,; represents the number of units shipped from
node i to node j.)
Min 4x14+8x24+5x34+7x15 +5x25…
A linear programming computer package is needed.
Hanson Inn is a 96-room hotel located near the airport and convention center in Louisville, Kentucky. When a convention or a special event is in town, Hanson increases its normal room rates and takes reservations based on a revenue management system. A large profesional organization has scheduled its annual convention in Louisville for the first weekend in June. Hanson Inn agreed to make at least 50% of its
rooms available for convention attendees at a special convention rate in order to be listed as a recommended hotel for the convention. Although the majority of attendees at the annual meeting typically request a Friday and Saturday two-night package, some attendees may select a Friday night only or a Saturday night only reservation. Customers not attending the convention may also request a Friday and
Saturday two-night package, or make a Friday night only or Saturday night only reservation. Thus, six types of reservations are…
Chapter 2 Solutions
A Transition to Advanced Mathematics
Ch. 2.1 - The Cayley tables for operations o,*,+, and are...Ch. 2.1 - Let m,n and M=A:A is an mn matrix with real number...Ch. 2.1 - Let be an associative operation on nonempty set A...Ch. 2.1 - Let be an associative operation on nonempty set A...Ch. 2.1 - Suppose that (A,*) is an algebraic system and * is...Ch. 2.1 - Let (A,o) be an algebra structure. An element lA...Ch. 2.1 - Let G be a group. Prove that if a2=e for all aG,...Ch. 2.1 - Give an example of an algebraic structure of order...Ch. 2.1 - Prob. 9ECh. 2.1 - Construct the operation table for each of the...
Ch. 2.1 - Prob. 11ECh. 2.1 - Prob. 12ECh. 2.1 - Suppose m and m2. Prove that 1 and m1 are distinct...Ch. 2.1 - Let m and a be natural numbers with am. Complete...Ch. 2.1 - Complete the proof of Theorem 6.1.4. First, show...Ch. 2.1 - Prob. 16ECh. 2.1 - Prob. 17ECh. 2.1 - Prob. 18ECh. 2.1 - Repeat Exercise 2 with the operation * given by...Ch. 2.2 - Prob. 1ECh. 2.2 - Let G be a group and aiG for all n. Prove that...Ch. 2.2 - Prove part (d) of Theorem 6.2.3. That is, prove...Ch. 2.2 - Prove part (b) of Theorem 6.2.4.Ch. 2.2 - List all generators of each cyclic group in...Ch. 2.2 - Let G be a group with identity e. Let aG. Prove...Ch. 2.2 - Let G be a group, and let H be a subgroup of G....Ch. 2.2 - Let ({0},) be the group of nonzero complex numbers...Ch. 2.2 - Prove that for every natural number m greater than...Ch. 2.2 - Show that the structure ({1},), with operation ...Ch. 2.2 - (a)In the group G of Exercise 2, find x such that...Ch. 2.2 - Show that (,), with operation # defined by...Ch. 2.2 - Prob. 13ECh. 2.2 - Prob. 14ECh. 2.2 - Prob. 15ECh. 2.2 - Show that each of the following algebraic...Ch. 2.2 - Prob. 17ECh. 2.2 - Given that G={e,u,v,w} is a group of order 4 with...Ch. 2.2 - Give an example of an algebraic system (G,o) that...Ch. 2.2 - (a)What is the order of S4, the symmetric group on...Ch. 2.3 - Find the order of the element 3 in each group....Ch. 2.3 - Find the order of each element of the group S3....Ch. 2.3 - Let 3 and 6 be the sets of integer multiples of 3...Ch. 2.3 - Let (3,+) and (6,+) be the groups in Exercise 10,...Ch. 2.3 - Let ({a,b,c},o) be the group with the operation...Ch. 2.3 - (a)Prove that the function f:1824 given by f(x)=4x...Ch. 2.3 - Define f:1512 by f(x)=4x. Prove that f is a...Ch. 2.3 - Let (G,) and (H,*) be groups, i be the identity...Ch. 2.3 - Show that (4,+) and ({1,1,i,i},) are isomorphic.Ch. 2.3 - Prove that every subgroup of a cyclic group is...Ch. 2.3 - Let G=a be a cyclic group of order 30. What is the...Ch. 2.3 - Assign a grade of A (correct), C (partially...Ch. 2.3 - Find all subgroups of (8,+). (U11,). (5,+). (U7,)....Ch. 2.3 - In the group S4, find two different subgroups that...Ch. 2.3 - Prove that if G is a group and H is a subgroup of...Ch. 2.3 - (a)Prove that if H and K are subgroups of a group...Ch. 2.3 - Let G be a group and H be a subgroup of G. If H is...Ch. 2.3 - Prove or disprove: Every abelian group is cyclic.Ch. 2.3 - Let G be a group. If H is a subgroup of G and K is...Ch. 2.4 - Define f:++ by f(x)=x where + is the set of all...Ch. 2.4 - Assign a grade of A (correct), C (partially...Ch. 2.4 - Define f: by f(x)=x3. Is f:(,+)(,+) operation...Ch. 2.4 - Define on by setting (a,b)(c,d)=(acbd,ad+bc)....Ch. 2.4 - Let f the set of all real-valued integrable...Ch. 2.4 - Prob. 6ECh. 2.4 - Let M be the set of all 22 matrices with real...Ch. 2.4 - Let Conj: be the conjugate mapping for complex...Ch. 2.4 - Prove the remaining parts of Theorem 6.4.1.Ch. 2.4 - Is S3 isomorphic to (6,+)? Explain.Ch. 2.4 - Prob. 11ECh. 2.4 - Use the method of proof of Cayley's Theorem to...Ch. 2.5 - Let (R,+,) be an algebraic structure such that...Ch. 2.5 - Assign a grade of A (correct), C (partially...Ch. 2.5 - Which of the following is a ring with the usual...Ch. 2.5 - Let [2] be the set {a+b2:a,b}. Define addition and...Ch. 2.5 - Complete the proof that for every m,(m+,) is a...Ch. 2.5 - Define addition and multiplication on the set ...Ch. 2.5 - Prob. 7ECh. 2.5 - Let (R,+,) be a ring and a,b,R. Prove that b+(a)...Ch. 2.5 - Prove the remaining parts of Theorem 6.5.3: For...Ch. 2.5 - Prob. 10ECh. 2.5 - Prob. 11ECh. 2.5 - Prob. 12ECh. 2.5 - Prob. 13ECh. 2.5 - Prob. 14ECh. 2.6 - Prob. 1ECh. 2.6 - Let A and B be subsets of . Prove that if sup(A)...Ch. 2.6 - (a)Give an example of sets A and B of real numbers...Ch. 2.6 - (a)Give an example of sets A and B of real numbers...Ch. 2.6 - Prob. 5ECh. 2.6 - Prob. 6ECh. 2.6 - Prob. 7ECh. 2.6 - Prob. 8ECh. 2.6 - Prob. 9ECh. 2.6 - Prob. 10ECh. 2.6 - Prob. 11ECh. 2.6 - Prob. 12ECh. 2.6 - Prob. 13ECh. 2.6 - Prob. 14ECh. 2.6 - Prob. 15ECh. 2.6 - Prob. 16ECh. 2.6 - Use the definition of “divides” to explain (a) why...Ch. 2.6 - Prob. 18ECh. 2.6 - Prob. 19ECh. 2.6 - Prob. 20ECh. 2.6 - For each function, find the value of f at 3 and...Ch. 2.6 - Let A be the set {1,2,3,4} and B={0,1,2,3}. Give a...Ch. 2.6 - Formulate and prove a characterization of greatest...Ch. 2.6 - Prob. 24ECh. 2.6 - Prob. 25E
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