Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
14th Edition
ISBN: 9780134675985
Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen, Christopher J. Stocker
Publisher: PEARSON
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Textbook Question
Chapter 5.3, Problem 56E
In Problems 49-64, construct a mathematical model in the form of a linear programming problem. (The answers in the back of the book for these application problems include the model.) Then solve by the geometric method.
Investment. An investor has
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Keity
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1. (i)
Identify which of the following subsets of R2 are open and which
are not.
(a)
A = (2,4) x (1, 2),
(b)
B = (2,4) x {1,2},
(c)
C = (2,4) x R.
Provide a sketch and a brief explanation to each of your answers.
[6 Marks]
(ii)
Give an example of a bounded set in R2 which is not open.
[2 Marks]
(iii)
Give an example of an open set in R2 which is not bounded.
[2 Marks
2.
(i)
Which of the following statements are true? Construct coun-
terexamples for those that are false.
(a)
sequence.
Every bounded sequence (x(n)) nEN C RN has a convergent sub-
(b)
(c)
(d)
Every sequence (x(n)) nEN C RN has a convergent subsequence.
Every convergent sequence (x(n)) nEN C RN is bounded.
Every bounded sequence (x(n)) EN CRN converges.
nЄN
(e)
If a sequence (xn)nEN C RN has a convergent subsequence, then
(xn)nEN is convergent.
[10 Marks]
(ii)
Give an example of a sequence (x(n))nEN CR2 which is located on
the parabola x2 = x², contains infinitely many different points and converges
to the limit x = (2,4).
[5 Marks]
2.
(i) What does it mean to say that a sequence (x(n)) nEN CR2
converges to the limit x E R²?
[1 Mark]
(ii) Prove that if a set ECR2 is closed then every convergent
sequence (x(n))nen in E has its limit in E, that is
(x(n)) CE and x() x
x = E.
[5 Marks]
(iii)
which is located on the parabola x2 = = x
x4, contains a subsequence that
Give an example of an unbounded sequence (r(n)) nEN CR2
(2, 16) and such that x(i)
converges to the limit x = (2, 16) and such that x(i)
#
x() for any i j.
[4 Marks
Chapter 5 Solutions
Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
Ch. 5.1 - In Step 2 of Example 1, 0,0 was used as a test...Ch. 5.1 - Graph 6x3y18.Ch. 5.1 - Graph (A) y4 (B) 4x9 (C) 3x2yCh. 5.1 - Find the linear inequality whose graph is given in...Ch. 5.1 - A food vendor at a rock concert sells hot dogs for...Ch. 5.1 - For Problems 1-8, if necessary, review Section...Ch. 5.1 - For Problems 1-8, if necessary, review Section...Ch. 5.1 - For Problems 1-8, if necessary, review Section...Ch. 5.1 - For Problems 1-8, if necessary, review Section...Ch. 5.1 - For Problems 1-8, if necessary, review Section...
Ch. 5.1 - For Problems 1-8, if necessary, review Section...Ch. 5.1 - For Problems 1-8, if necessary, review Section...Ch. 5.1 - For Problems 1-8, if necessary, review Section...Ch. 5.1 - Graph each inequality in Problems 9-18. yx1Ch. 5.1 - Graph each inequality in Problems 9-18. yx+1Ch. 5.1 - Graph each inequality in Problems 9-18. 3x2y6Ch. 5.1 - Graph each inequality in Problems 9-18. 2x5y10Ch. 5.1 - Graph each inequality in Problems 9-18. x4Ch. 5.1 - Graph each inequality in Problems 9-18. y5Ch. 5.1 - Graph each inequality in Problems 9-18. 6x+4y24Ch. 5.1 - Graph each inequality in Problems 9-18. 4x+8y32Ch. 5.1 - Graph each inequality in Problems 9-18. 5x2yCh. 5.1 - Graph each inequality in Problems 9-18. 6x4yCh. 5.1 - In Problems 19-22, (A) graph the set of points...Ch. 5.1 - In Problems 19-22, (A) graph the set of points...Ch. 5.1 - In Problems 19-22, (A) graph the set of points...Ch. 5.1 - In Problems 19-22, (A) graph the set of points...Ch. 5.1 - In Problems 23-32, define the variable and...Ch. 5.1 - In Problems 23-32, define the variable and...Ch. 5.1 - In Problems 23-32, define the variable and...Ch. 5.1 - In Problems 23-32, define the variable and...Ch. 5.1 - In Problems 23-32, define the variable and...Ch. 5.1 - In Problems 23-32, define the variable and...Ch. 5.1 - In Problems 23-32, define the variable and...Ch. 5.1 - In Problems 23-32, define the variable and...Ch. 5.1 - \ In Problems 23-32, define the variable and...Ch. 5.1 - In Problems 23-32, define the variable and...Ch. 5.1 - In Exercises 33-38, state the linear inequality...Ch. 5.1 - In Exercises 33-38, state the linear inequality...Ch. 5.1 - In Exercises 33-38, state the linear inequality...Ch. 5.1 - In Exercises 33-38, state the linear inequality...Ch. 5.1 - In Exercises 33-38, state the linear inequality...Ch. 5.1 - In Exercises 33-38, state the linear inequality...Ch. 5.1 - In Problems 39-44, define two variables and...Ch. 5.1 - In Problems 39-44, define two variables and...Ch. 5.1 - In Problems 39-44, define two variables and...Ch. 5.1 - In Problems 39-44, define two variables and...Ch. 5.1 - In Problems 39-44, define two variables and...Ch. 5.1 - In Problems 39-44, define two variables and...Ch. 5.1 - In Problems 45-54, graph each inequality subject...Ch. 5.1 - In Problems 45-54, graph each inequality subject...Ch. 5.1 - In Problems 45-54, graph each inequality subject...Ch. 5.1 - In Problems 45-54, graph each inequality subject...Ch. 5.1 - In Problems 45-54, graph each inequality subject...Ch. 5.1 - In Problems 45-54, graph each inequality subject...Ch. 5.1 - In Problems 45-54, graph each inequality subject...Ch. 5.1 - In Problems 45-54, graph each inequality subject...Ch. 5.1 - In Problems 45-54, graph each inequality subject...Ch. 5.1 - In Problems 45-54, graph each inequality subject...Ch. 5.1 - In Problems 55-66, express your answer as a linear...Ch. 5.1 - In Problems 55-66, express your answer as a linear...Ch. 5.1 - In Problems 55-66, express your answer as a linear...Ch. 5.1 - In Problems 55-66, express your answer as a linear...Ch. 5.1 - In Problems 55-66, express your answer as a linear...Ch. 5.1 - In Problems 55-66, express your answer as a linear...Ch. 5.1 - In Problems 55-66, express your answer as a linear...Ch. 5.1 - In Problems 55-66, express your answer as a linear...Ch. 5.1 - In Problems 55-66, express your answer as a linear...Ch. 5.1 - In Problems 55-66, express your answer as a linear...Ch. 5.1 - In Problems 55-66, express your answer as a linear...Ch. 5.1 - In Problems 55-66, express your answer as a linear...Ch. 5.2 - Determine whether the solution region of each...Ch. 5.2 - Solve the following system of linear inequalities...Ch. 5.2 - Solve the following system of linear inequalities...Ch. 5.2 - A manufacturing plant makes two types of...Ch. 5.2 - For Problems 1-8, if necessary, review Section...Ch. 5.2 - For Problems 1-8, if necessary, review Section...Ch. 5.2 - For Problems 1-8, if necessary, review Section...Ch. 5.2 - For Problems 1-8, if necessary, review Section...Ch. 5.2 - For Problems 1-8, if necessary, review Section...Ch. 5.2 - For Problems 1-8, if necessary, review Section...Ch. 5.2 - For Problems 1-8, if necessary, review Section...Ch. 5.2 - For Problems 1-8, if necessary, review Section...Ch. 5.2 - In Problems 9-12, match the solution region of...Ch. 5.2 - In Problems 9-12, match the solution region of...Ch. 5.2 - In Problems 9-12, match the solution region of...Ch. 5.2 - In Problems 9-12, match the solution region of...Ch. 5.2 - In Problems 13-16, solve each system of linear...Ch. 5.2 - In Problems 13-16, solve each system of linear...Ch. 5.2 - In Problems 13-16, solve each system of linear...Ch. 5.2 - In Problems 13-16, solve each system of linear...Ch. 5.2 - In Problems 17-20, match the solution region of...Ch. 5.2 - In Problems 17-20, match the solution region of...Ch. 5.2 - In Problems 17-20, match the solution region of...Ch. 5.2 - In Problems 17-20, match the solution region of...Ch. 5.2 - In Problems 21-28, is the solution region bounded...Ch. 5.2 - In Problems 21-28, is the solution region bounded...Ch. 5.2 - In Problems 21-28, is the solution region bounded...Ch. 5.2 - In Problems 21-28, is the solution region bounded...Ch. 5.2 - In Problems 21-28, is the solution region bounded...Ch. 5.2 - In Problems 21-28, is the solution region bounded...Ch. 5.2 - In Problems 21-28, is the solution region bounded...Ch. 5.2 - In Problems 21-28, is the solution region bounded...Ch. 5.2 - Solve the systems in Problems 29-38 graphically...Ch. 5.2 - Solve the systems in Problems 29-38 graphically...Ch. 5.2 - Solve the systems in Problems 29-38 graphically...Ch. 5.2 - Solve the systems in Problems 29-38 graphically...Ch. 5.2 - Solve the systems in Problems 29-38 graphically...Ch. 5.2 - Solve the systems in Problems 29-38 graphically...Ch. 5.2 - Solve the systems in Problems 29-38 graphically...Ch. 5.2 - Solve the systems in Problems 29-38 graphically...Ch. 5.2 - Solve the systems in Problems 29-38 graphically...Ch. 5.2 - Solve the systems in Problems 29-38 graphically...Ch. 5.2 - Solve the systems in Problems 39-48 graphically...Ch. 5.2 - Solve the systems in Problems 39-48 graphically...Ch. 5.2 - Solve the systems in Problems 39-48 graphically...Ch. 5.2 - \ Solve the systems in Problems 39-48 graphically...Ch. 5.2 - Solve the systems in Problems 39-48 graphically...Ch. 5.2 - Solve the systems in Problems 39-48 graphically...Ch. 5.2 - Solve the systems in Problems 39-48 graphically...Ch. 5.2 - Solve the systems in Problems 39-48 graphically...Ch. 5.2 - Solve the systems in Problems 39-48 graphically...Ch. 5.2 - Solve the systems in Problems 39-48 graphically...Ch. 5.2 - Problems 49 and 50 introduce an algebraic process...Ch. 5.2 - Problems 49 and 50 introduce an algebraic process...Ch. 5.2 - Water skis. A manufacturing company makes two...Ch. 5.2 - Furniture. A furniture manufacturing company...Ch. 5.2 - Water skis. Refer to Problem 51. The company makes...Ch. 5.2 - Furniture. Refer to Problem 52. The company makes...Ch. 5.2 - Plant food. A farmer can buy two types of plant...Ch. 5.2 - Nutrition. A dietician in a hospital is to arrange...Ch. 5.2 - Psychology. A psychologist uses two types of boxes...Ch. 5.3 - A manufacturing plant makes two types of...Ch. 5.3 - Refer to the feasible region S shown in Figure 3....Ch. 5.3 - In Example 2B we saw that there was no optimal...Ch. 5.3 - (A) Maximize and minimize z=4x+2y subject to the...Ch. 5.3 - A chicken farmer can buy a special food mix A at...Ch. 5.3 - In Problem 1-8, if necessary, review Theorem 1. In...Ch. 5.3 - In Problem 1-8, if necessary, review Theorem 1. In...Ch. 5.3 - In Problem 1-8, if necessary, review Theorem 1. In...Ch. 5.3 - In Problem 1-8, if necessary, review Theorem 1. In...Ch. 5.3 - In Problems 1-8, if necessary, review Theorem 1....Ch. 5.3 - In Problems 1-8, if necessary, review Theorem 1....Ch. 5.3 - In Problems 1-8, if necessary, review Theorem 1....Ch. 5.3 - In Problems 1-8, if necessary, review Theorem 1....Ch. 5.3 - In Problems 9-12, graph the constant-profit lines...Ch. 5.3 - In Problems 9-12, graph the constant-profit lines...Ch. 5.3 - In Problems 9-12, graph the constant-profit lines...Ch. 5.3 - In Problems 9-12, graph the constant-profit lines...Ch. 5.3 - In Problems 13-16, graph the constant-cost lines...Ch. 5.3 - In Problems 13-16, graph the constant-cost lines...Ch. 5.3 - In Problems 13-16, graph the constant-cost lines...Ch. 5.3 - In Problems 13-16, graph the constant-cost lines...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - In Problems 39 and 40, explain why Theorem 2...Ch. 5.3 - In Problems 39 and 40, explain why Theorem 2...Ch. 5.3 - Problems 41-48 refer to the bounded feasible...Ch. 5.3 - Problems 41-48 refer to the bounded feasible...Ch. 5.3 - Problems 41-48 refer to the bounded feasible...Ch. 5.3 - Problems 41-48 refer to the bounded feasible...Ch. 5.3 - Problems 41-48 refer to the bounded feasible...Ch. 5.3 - Problems 41-48 refer to the bounded feasible...Ch. 5.3 - Problems 41-48 refer to the bounded feasible...Ch. 5.3 - Problems 41-48 refer to the bounded feasible...Ch. 5.3 - In Problems 49-64, construct a mathematical model...Ch. 5.3 - In Problems 49-64, construct a mathematical model...Ch. 5.3 - In Problems 49-64, construct a mathematical model...Ch. 5.3 - In Problems 49-64, construct a mathematical model...Ch. 5.3 - In Problems 49-64, construct a mathematical model...Ch. 5.3 - In Problems 49-64, construct a mathematical model...Ch. 5.3 - In Problems 49-64, construct a mathematical model...Ch. 5.3 - In Problems 49-64, construct a mathematical model...Ch. 5.3 - In Problems 49-64, construct a mathematical model...Ch. 5.3 - In Problems 49-64, construct a mathematical model...Ch. 5.3 - In Problems 49-64, construct a mathematical model...Ch. 5.3 - In Problems 49-64, construct a mathematical model...Ch. 5.3 - In Problems 49-64, construct a mathematical model...Ch. 5.3 - In Problems 49-64, construct a mathematical model...Ch. 5.3 - In Problems 49-64, construct a mathematical model...Ch. 5.3 - In Problems 49-64, construct a mathematical model...Ch. 5 - Graph each inequality. x2y3Ch. 5 - Graph each inequality. 3y5x30Ch. 5 - Graph the systems in Problems 3-6 and indicate...Ch. 5 - Graph the systems in Problems 3-6 and indicate...Ch. 5 - Graph the systems in Problems 3-6 and indicate...Ch. 5 - Graph the systems in Problems 3-6 and indicate...Ch. 5 - In Exercises 7 and 8, state the linear inequality...Ch. 5 - In Exercises 7 and 8, state the linear inequality...Ch. 5 - Solve the linear programming problems in Problems...Ch. 5 - Solve the linear programming problems in Problems...Ch. 5 - Solve the linear programming problems in Problems...Ch. 5 - Solve the linear programming problems in Problems...Ch. 5 - Solve the linear programming problems in Problems...Ch. 5 - Electronics. 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