Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
13th Edition
ISBN: 9780321945525
Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen
Publisher: PEARSON
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Textbook Question
Chapter 6.3, Problem 34E
A minimization problem has
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these are solutions to a tutorial that was done and im a little lost. can someone please explain to me how these iterations function, for example i Do not know how each set of matrices produces a number if someine could explain how its done and provide steps it would be greatly appreciated thanks.
Q1) Classify the following statements as a true or false statements
a. Any ring with identity is a finitely generated right R module.-
b. An ideal 22 is small ideal in Z
c. A nontrivial direct summand of a module cannot be large or small submodule
d. The sum of a finite family of small submodules of a module M is small in M
A module M 0 is called directly indecomposable if and only if 0 and M are
the only direct summands of M
f. A monomorphism a: M-N is said to split if and only if Ker(a) is a direct-
summand in M
& Z₂ contains no minimal submodules
h. Qz is a finitely generated module
i. Every divisible Z-module is injective
j. Every free module is a projective module
Q4) Give an example and explain your claim in each case
a) A module M which has two composition senes 7
b) A free subset of a modale
c) A free module
24
d) A module contains a direct summand submodule 7,
e) A short exact sequence of modules 74.
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Q.1) Classify the following statements as a true or false statements:
a. If M is a module, then every proper submodule of M is contained in a maximal
submodule of M.
b. The sum of a finite family of small submodules of a module M is small in M.
c. Zz is directly indecomposable.
d. An epimorphism a: M→ N is called solit iff Ker(a) is a direct summand in M.
e. The Z-module has two composition series.
Z
6Z
f. Zz does not have a composition series.
g. Any finitely generated module is a free module.
h. If O→A MW→ 0 is short exact sequence then f is epimorphism.
i. If f is a homomorphism then f-1 is also a homomorphism.
Maximal C≤A if and only if is simple.
Sup
Q.4) Give an example and explain your claim in each case:
Monomorphism not split.
b) A finite free module.
c) Semisimple module.
d) A small submodule A of a module N and a homomorphism op: MN, but
(A) is not small in M.
Chapter 6 Solutions
Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
Ch. 6.1 - The following linear programming problem has only...Ch. 6.1 - Find an example of a standard maximization problem...Ch. 6.1 - Use the table method to solve the following linear...Ch. 6.1 - Refer to Example 1. Find the basic solution for...Ch. 6.1 - Construct the table of basic solutions and use it...Ch. 6.1 - Construct the table of basic solutions and use it...Ch. 6.1 - Refer to Table 5. For the basic solution...Ch. 6.1 - Prob. 1ECh. 6.1 - Prob. 2ECh. 6.1 - Prob. 3E
Ch. 6.1 - Prob. 4ECh. 6.1 - Problems 9-12 refer to the system...Ch. 6.1 - Problems 9-12 refer to the system...Ch. 6.1 - Problems 9-12 refer to the system...Ch. 6.1 - Problems 9-12 refer to the system...Ch. 6.1 - In Problems 13-20, write the e-system obtained via...Ch. 6.1 - In Problems 13-20, write the e-system obtained via...Ch. 6.1 - In Problems 13-20, write the e-system obtained via...Ch. 6.1 - In Problems 13-20, write the e-system obtained via...Ch. 6.1 - In Problems 13-20, write the e-system obtained via...Ch. 6.1 - In Problems 13-20, write the e-system obtained via...Ch. 6.1 - In Problems 13-20, write the e-system obtained via...Ch. 6.1 - In Problems 13-20, write the e-system obtained via...Ch. 6.1 - Problems 21-30 refer to the table below of the six...Ch. 6.1 - Problems 21-30 refer to the table below of the six...Ch. 6.1 - Problems 21-30 refer to the table below of the six...Ch. 6.1 - Problems 21-30 refer to the table below of the six...Ch. 6.1 - Prob. 21ECh. 6.1 - Prob. 22ECh. 6.1 - Problems 21-30 refer to the table below of the six...Ch. 6.1 - Problems 21-30 refer to the table below of the six...Ch. 6.1 - Problems 21-30 refer to the table below of the six...Ch. 6.1 - Problems 21-30 refer to the table below of the six...Ch. 6.1 - Problems 31-40 refer to the partially completed...Ch. 6.1 - Problems 31-40 refer to the partially completed...Ch. 6.1 - Problems 31-40 refer to the partially completed...Ch. 6.1 - Problems 31-40 refer to the partially completed...Ch. 6.1 - Problems 31-40 refer to the partially completed...Ch. 6.1 - Problems 31-40 refer to the partially completed...Ch. 6.1 - Problems 31-40 refer to the partially completed...Ch. 6.1 - Problems 31-40 refer to the partially completed...Ch. 6.1 - Problems 31-40 refer to the partially completed...Ch. 6.1 - Problems 31-40 refer to the partially completed...Ch. 6.1 - In Problems 41-48, convert the given i-system to...Ch. 6.1 - In Problems 41-48, convert the given i-system to...Ch. 6.1 - In Problems 41-48, convert the given i-system to...Ch. 6.1 - In Problems 41-48, convert the given i-system to...Ch. 6.1 - In Problems 41-48, convert the given i-system to...Ch. 6.1 - In Problems 41-48, convert the given i-system to...Ch. 6.1 - In Problems 41-48, convert the given i-system to...Ch. 6.1 - In Problems 41-48, convert the given i-system to...Ch. 6.1 - In Problems 45-50, graph the system of...Ch. 6.1 - In Problems 45-50, graph the system of...Ch. 6.1 - In Problems 45-50, graph the system of...Ch. 6.1 - In Problems 45-50, graph the system of...Ch. 6.1 - In Problems 45-50, graph the system of...Ch. 6.1 - In Problems 45-50, graph the system of...Ch. 6.1 - In Problems 59-66, solve the given linear...Ch. 6.1 - In Problems 59-66, solve the given linear...Ch. 6.1 - In Problems 59-66, solve the given linear...Ch. 6.1 - In Problems 59-66, solve the given linear...Ch. 6.1 - In Problems 59-66, solve the given linear...Ch. 6.1 - In Problems 59-66, solve the given linear...Ch. 6.1 - In Problems 59-66, solve the given linear...Ch. 6.1 - In Problems 59-66, solve the given linear...Ch. 6.1 - A linear programming problem has four decision...Ch. 6.1 - A linear programming problem has five decision...Ch. 6.1 - A linear programming problem has 30 decision...Ch. 6.1 - A linear programming problem has 40 decision...Ch. 6.2 - Graph the feasible region for the linear...Ch. 6.2 - Solve the following linear programming problem...Ch. 6.2 - Solve using the simplex method:...Ch. 6.2 - Repeat Example 3 modified as follows:Ch. 6.2 - For the simplex tableau in Problems 1-4, (A)...Ch. 6.2 - For the simplex tableau in Problems 1-4, (A)...Ch. 6.2 - For the simplex tableau in Problems 1-4, (A)...Ch. 6.2 - For the simplex tableau in Problems 1-4, (A)...Ch. 6.2 - In Problems 5-8, find the pivot element, identify...Ch. 6.2 - In Problems 5-8, find the pivot element, identify...Ch. 6.2 - In Problems 5-8, find the pivot element, identify...Ch. 6.2 - In Problems 5-8, find the pivot element, identify...Ch. 6.2 - In Problems 9-12, (A) Using the slack variables,...Ch. 6.2 - In Problems 9-12, (A) Using the slack variables,...Ch. 6.2 - In Problems 9-12, (A) Using the slack variables,...Ch. 6.2 - In Problems 9-12, (A) Using the slack variables,...Ch. 6.2 - Solve the linear programming problems in Problems...Ch. 6.2 - Solve the linear programming problems in Problems...Ch. 6.2 - Solve the linear programming problems in Problems...Ch. 6.2 - Solve the linear programming problems in Problems...Ch. 6.2 - Solve the linear programming problems in Problems...Ch. 6.2 - Solve the linear programming problems in Problems...Ch. 6.2 - Solve the linear programming problems in Problems...Ch. 6.2 - Solve the linear programming problems in Problems...Ch. 6.2 - Solve the linear programming problems in Problems...Ch. 6.2 - Solve the linear programming problems in Problems...Ch. 6.2 - Solve the linear programming problems in Problems...Ch. 6.2 - Solve the linear programming problems in Problems...Ch. 6.2 - Solve the linear programming problems in Problems...Ch. 6.2 - Solve the linear programming problems in Problems...Ch. 6.2 - Solve the linear programming problems in Problems...Ch. 6.2 - Solve the linear programming problems in Problems...Ch. 6.2 - In Problems 33 and 34, first solve the linear...Ch. 6.2 - In Problems 33 and 34, first solve the linear...Ch. 6.2 - Solve Problems 35 and 36 by the simplex method and...Ch. 6.2 - Solve Problems 35 and 36 by the simplex method and...Ch. 6.2 - In Problems 37-40, there is a tie for the choice...Ch. 6.2 - In Problems 37-40, there is a tie for the choice...Ch. 6.2 - In Problems 37-40, there is a tie for the choice...Ch. 6.2 - In Problems 37-40, there is a tie for the choice...Ch. 6.2 - In Problems 41-56, construct a mathematical model...Ch. 6.2 - In Problems 41-56, construct a mathematical model...Ch. 6.2 - In Problems 41-56, construct a mathematical model...Ch. 6.2 - In Problems 41-56, construct a mathematical model...Ch. 6.2 - In Problems 41-56, construct a mathematical model...Ch. 6.2 - In Problems 41-56, construct a mathematical model...Ch. 6.2 - In Problems 41-56, construct a mathematical model...Ch. 6.2 - In Problems 41-56, construct a mathematical model...Ch. 6.2 - In Problems 41-56, construct a mathematical model...Ch. 6.2 - In Problems 41-56, construct a mathematical model...Ch. 6.2 - In Problems 41-56, construct a mathematical model...Ch. 6.2 - In Problems 41-56, construct a mathematical model...Ch. 6.2 - In Problems 41-56, construct a mathematical model...Ch. 6.2 - In Problems 41-56, construct a mathematical model...Ch. 6.2 - In Problems 41-56, construct a mathematical model...Ch. 6.2 - In Problems 41-56, construct a mathematical model...Ch. 6.3 - Excluding the nonnegative constraints, the...Ch. 6.3 - The simplex method can be used to solve any...Ch. 6.3 - Form the dual problem:...Ch. 6.3 - Solve the following minimization problem by...Ch. 6.3 - Solve the following minimization problem by...Ch. 6.3 - Repeat Example 4 if the shipping charge from plant...Ch. 6.3 - In Problems 1-8, find the transpose of each...Ch. 6.3 - In Problems 1-8, find the transpose of each...Ch. 6.3 - In Problems 1-8, find the transpose of each...Ch. 6.3 - In Problems 1-8, find the transpose of each...Ch. 6.3 - In Problems 1-8, find the transpose of each...Ch. 6.3 - In Problems 1-8, find the transpose of each...Ch. 6.3 - In Problems 1-8, find the transpose of each...Ch. 6.3 - In Problems 1-8, find the transpose of each...Ch. 6.3 - In Problems 9 and 10, (A) Form the dual problem....Ch. 6.3 - In Problems 9 and 10, (A) Form the dual problem....Ch. 6.3 - In Problems 11 and 12, a minimization problem, the...Ch. 6.3 - In Problems 11 and 12, a minimization problem, the...Ch. 6.3 - In Problems 13-20, (A) Form the dual problem. (B)...Ch. 6.3 - In Problems 13-20, (A) Form the dual problem. (B)...Ch. 6.3 - In Problems 13-20, (A) Form the dual problem. (B)...Ch. 6.3 - In Problems 13-20, (A) Form the dual problem. (B)...Ch. 6.3 - In Problems 13-20, (A) Form the dual problem. (B)...Ch. 6.3 - In Problems 13-20, (A) Form the dual problem. (B)...Ch. 6.3 - In Problems 13-20, (A) Form the dual problem. (B)...Ch. 6.3 - In Problems 13-20, (A) Form the dual problem. (B)...Ch. 6.3 - Solve the linear programming problems in Problem...Ch. 6.3 - Solve the linear programming problems in Problem...Ch. 6.3 - Solve the linear programming problems in Problem...Ch. 6.3 - Solve the linear programming problems in Problem...Ch. 6.3 - Solve the linear programming problems in Problem...Ch. 6.3 - Solve the linear programming problems in Problem...Ch. 6.3 - Solve the linear programming problems in Problem...Ch. 6.3 - Solve the linear programming problems in Problem...Ch. 6.3 - Solve the linear programming problems in Problem...Ch. 6.3 - Solve the linear programming problems in Problem...Ch. 6.3 - Solve the linear programming problems in Problem...Ch. 6.3 - Solve the linear programming problems in Problem...Ch. 6.3 - A minimization problem has 4 variables and 2...Ch. 6.3 - A minimization problem has 3 variables and 5...Ch. 6.3 - If you want to solve a minimization problem by...Ch. 6.3 - If you want to solve a minimization problem by...Ch. 6.3 - In Problems 37-40, determine whether a...Ch. 6.3 - In Problems 37-40, determine whether a...Ch. 6.3 - In Problems 37-40, determine whether a...Ch. 6.3 - In Problems 37-40, determine whether a...Ch. 6.3 - Solve the linear programming problem in Problems...Ch. 6.3 - Solve the linear programming problem in Problems...Ch. 6.3 - Solve the linear programming problem in Problems...Ch. 6.3 - Solve the linear programming problem in Problems...Ch. 6.3 - In Problems 49-58, construct a mathematical model...Ch. 6.3 - In Problems 49-58, construct a mathematical model...Ch. 6.3 - In Problems 49-58, construct a mathematical model...Ch. 6.3 - In Problems 49-58, construct a mathematical model...Ch. 6.3 - In Problems 49-58, construct a mathematical model...Ch. 6.3 - In Problems 49-58, construct a mathematical model...Ch. 6.3 - In Problems 49-58, construct a mathematical model...Ch. 6.3 - In Problems 49-58, construct a mathematical model...Ch. 6.3 - In Problems 49-58, construct a mathematical model...Ch. 6.3 - In Problems 49-58, construct a mathematical model...Ch. 6.4 - Repeat Example 1 for...Ch. 6.4 - Solve the following linear programming problem...Ch. 6.4 - Solve the following linear programming problem...Ch. 6.4 - Prob. 4MPCh. 6.4 - Suppose that the refinery in Example 5 has 35,000...Ch. 6.4 - In Problems 1-8, (A) Introduce slack, surplus, and...Ch. 6.4 - In Problems 1-8, (A) Introduce slack, surplus, and...Ch. 6.4 - In Problems 1-8, (A) Introduce slack, surplus, and...Ch. 6.4 - In Problems 1-8, (A) Introduce slack, surplus, and...Ch. 6.4 - In Problems 1-8, (A) Introduce slack, surplus, and...Ch. 6.4 - In Problems 1-8, (A) Introduce slack, surplus, and...Ch. 6.4 - In Problems 1-8, (A) Introduce slack, surplus, and...Ch. 6.4 - In Problems 1-8, (A) Introduce slack, surplus, and...Ch. 6.4 - Use the big M method to solve Problems 9-22....Ch. 6.4 - Use the big M method to solve Problems 9-22....Ch. 6.4 - Use the big M method to solve Problems 9-22....Ch. 6.4 - Use the big M method to solve Problems 9-22....Ch. 6.4 - Use the big M method to solve Problems 9-22....Ch. 6.4 - Use the big M method to solve Problems 9-22....Ch. 6.4 - Use the big M method to solve Problems 9-22....Ch. 6.4 - Use the big M method to solve Problems 9-22....Ch. 6.4 - Use the big M method to solve Problems 9-22....Ch. 6.4 - Use the big M method to solve Problems 9-22....Ch. 6.4 - Use the big M method to solve Problems 9-22....Ch. 6.4 - Use the big M method to solve Problems 9-22....Ch. 6.4 - Use the big M method to solve Problems 9-22....Ch. 6.4 - Use the big M method to solve Problems 9-22....Ch. 6.4 - Solve Problems 5 and 7 by graphing (the geometric...Ch. 6.4 - Solve Problems 6 and 8 by graphing (the geometric...Ch. 6.4 - Problems 25-32 are mixed. Some can be solved by...Ch. 6.4 - Problems 25-32 are mixed. Some can be solved by...Ch. 6.4 - Problems 25-32 are mixed. Some can be solved by...Ch. 6.4 - Problems 25-32 are mixed. Some can be solved by...Ch. 6.4 - Problems 25-32 are mixed. Some can be solved by...Ch. 6.4 - Problems 25-32 are mixed. Some can be solved by...Ch. 6.4 - Problems 25-32 are mixed. Some can be solved by...Ch. 6.4 - Problems 25-32 are mixed. Some can be solved by...Ch. 6.4 - In Problems 33-38, construct a mathematical model...Ch. 6.4 - In Problems 33-38, construct a mathematical model...Ch. 6.4 - In Problems 33-38, construct a mathematical model...Ch. 6.4 - In Problems 33-38, construct a mathematical model...Ch. 6.4 - In Problems 33-38, construct a mathematical model...Ch. 6.4 - In Problems 33-38, construct a mathematical model...Ch. 6.4 - In Problems 39-47, construct a mathematical model...Ch. 6.4 - In Problems 39-47, construct a mathematical model...Ch. 6.4 - In Problems 39-47, construct a mathematical model...Ch. 6.4 - In Problems 39-47, construct a mathematical model...Ch. 6.4 - In Problems 39-47, construct a mathematical model...Ch. 6.4 - In Problems 39-47, construct a mathematical model...Ch. 6.4 - In Problems 39-47, construct a mathematical model...Ch. 6.4 - In Problems 39-47, construct a mathematical model...Ch. 6.4 - In Problems 39-47, construct a mathematical model...Ch. 6 - Given the linear programming problem...Ch. 6 - How many basic variables and how many nonbasic...Ch. 6 - Find all basic solutions for the system in Problem...Ch. 6 - Write the simplex tableau for Problem 9, and...Ch. 6 - Solve Problem 9 using the simplex method.Ch. 6 - For the simplex tableau below, identify the basic...Ch. 6 - Find the basic solution for each tableau....Ch. 6 - Form the dual problem of...Ch. 6 - Write the initial system for the dual problem in...Ch. 6 - Write the first simplex tableau for the dual...Ch. 6 - Use the simplex method to find the optimal...Ch. 6 - Use the final simplex tableau from Problem 19 to...Ch. 6 - Solve the linear programming problem using the...Ch. 6 - Form the dual problem of the linear programming...Ch. 6 - Solve Problem 22 by applying the simplex method to...Ch. 6 - Solve the linear programming Problems 24 and...Ch. 6 - Solve the linear programming Problems 24 and...Ch. 6 - In problems 28 and 29, (A) Introduce slack,...Ch. 6 - In problems 28 and 29, (A) Introduce slack,...Ch. 6 - Find the modified problem for the following linear...Ch. 6 - Write a brief verbal description of the type of...Ch. 6 - Write a brief verbal description of the type of...Ch. 6 - Write a brief verbal description of the type of...Ch. 6 - Solve the following linear programming problem by...Ch. 6 - Solve by the dual problem method:...Ch. 6 - Solve Problem 35 by the big M method.Ch. 6 - Solve by the dual problem method:...Ch. 6 - In problems 38-41, construct a mathematical model...Ch. 6 - In problems 38-41, construct a mathematical model...Ch. 6 - In problems 38-41, construct a mathematical model...Ch. 6 - In problems 38-41, construct a mathematical model...
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