Finite Mathematics (11th Edition)
11th Edition
ISBN: 9780321979438
Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey
Publisher: PEARSON
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Textbook Question
Chapter 4.2, Problem 27E
Set up and solve Exercises 23–29 by the simplex method.
APPLY IT Manufacturing Bicycles A manufacturer of bicycles builds racing, touring, and mountain models. The bicycles are made of both steel and aluminum. The company has available 91,800 units of steel and 42,000 units of aluminum. The racing, touring, and mountain models need 17, 27, and 34 units of steel, and 12, 21, and 15 units of aluminum, respectively. (See Exercise 28 in Section 4.1.)
(a) How many of each type of should be made in order to maximize profit if the company makes $8 per racing bike, $12 per touring bike, and $22 per mountain bike?
(b) What is the maximum possible profit?
(c) Does it require all of the available units of steel and aluminum to build the bicycles that produce the maximum profit? If not, how much of each material is left over? Compare any leftover to the value of the relevant slack variable.
(d) There are many unstated assumptions in the problem given above. Even if the mathematical solution is to make only one or two types of the bicycles, there may be demand for the type(s) not being made, which would create problems for the company. Discuss this and other difficulties that would arise in real situation.
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1. The CLT provides an approximate sampling distribution for the arithmetic average Ỹ of a
random sample Y₁, . . ., Yn f(y). The parameters of the approximate sampling distribution
depend on the mean and variance of the underlying random variables (i.e., the population
mean and variance). The approximation can be written to emphasize this, using the expec-
tation and variance of one of the random variables in the sample instead of the parameters
μ, 02:
YNEY,
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(EY,, varyi
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For the following population distributions f, write the approximate distribution of the sample
mean.
(a) Exponential with rate ẞ: f(y) = ß exp{−ßy}
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(b) Chi-square with degrees of freedom: f(y) = ( 4 ) 2 y = exp { — ½/ }
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(c) Poisson with rate λ: P(Y = y) = exp(-\}
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Chapter 4 Solutions
Finite Mathematics (11th Edition)
Ch. 4.1 - Convert each inequality into an equation by adding...Ch. 4.1 - Prob. 2ECh. 4.1 - Convert each inequality into an equation by adding...Ch. 4.1 - Prob. 4ECh. 4.1 - For Exercises 5-8. (a) determine the number of...Ch. 4.1 - Prob. 6ECh. 4.1 - For Exercises 5-8, (a) determine the number of...Ch. 4.1 - For Exercises 5-8, (a) determine the number of...Ch. 4.1 -
Introduce slack variables as necessary, then...Ch. 4.1 - Introduce slack variables as necessary, then write...
Ch. 4.1 - Introduce slack variables as necessary, then write...Ch. 4.1 - Introduce slack variables as necessary, then write...Ch. 4.1 - Prob. 13ECh. 4.1 - Introduce slack variables as necessary, then write...Ch. 4.1 -
Write the solutions that can be read from each...Ch. 4.1 - Write the solutions that can be read from each...Ch. 4.1 - Prob. 17ECh. 4.1 - Prob. 18ECh. 4.1 - Pivot once as indicated in each simplex tableau....Ch. 4.1 - Pivot once as indicated in each simplex tableau....Ch. 4.1 - Prob. 21ECh. 4.1 - Prob. 22ECh. 4.1 - Prob. 23ECh. 4.1 - Prob. 24ECh. 4.1 - Explain the purpose of a slack variable.Ch. 4.1 - Prob. 26ECh. 4.1 - Prob. 27ECh. 4.1 - Set up Exercises 2731 for solution by the simplex...Ch. 4.1 - Set up Exercises 2731 for solution by the simplex...Ch. 4.1 - Set up Exercises 2731 for solution by the simplex...Ch. 4.1 - Set up Exercises 27for solution by the simplex...Ch. 4.2 -
In Exercises 1-6, the initial tableau of a linear...Ch. 4.2 -
In Exercises 1-6, the initial tableau of a linear...Ch. 4.2 - In Exercises 1-6, the initial tableau of a linear...Ch. 4.2 - In Exercises 1-6, the initial tableau of a linear...Ch. 4.2 -
In Exercises 1-6, the initial tableau of a linear...Ch. 4.2 - In Exercises 1- the initial tableau of a linear...Ch. 4.2 -
Use the simplex method to solve each linear...Ch. 4.2 - Prob. 8ECh. 4.2 - Prob. 9ECh. 4.2 - Use the simplex method to solve each linear...Ch. 4.2 - Prob. 11ECh. 4.2 - Prob. 12ECh. 4.2 -
Use the simplex method to solve each linear...Ch. 4.2 - Prob. 14ECh. 4.2 - Use the simplex method to solve each linear...Ch. 4.2 - Prob. 16ECh. 4.2 - Prob. 17ECh. 4.2 - Prob. 18ECh. 4.2 - The simplex algorithm still works if an indicator...Ch. 4.2 -
20. What goes wrong if a quotient other than...Ch. 4.2 - Prob. 21ECh. 4.2 - Prob. 22ECh. 4.2 - Prob. 23ECh. 4.2 -
Set up and solve Exercises 23–29 by the...Ch. 4.2 -
Set up and solve Exercises 23–29 by the simplex...Ch. 4.2 - Set up and solve Exercises 23–29 by the simplex...Ch. 4.2 - Set up and solve Exercises 2329 by the simplex...Ch. 4.2 - Set up and solve Exercises 2329 by the simplex...Ch. 4.2 - Prob. 29ECh. 4.2 - Profit A manufacturer makes two products, toy...Ch. 4.2 - Exercises and 32 come from past CPA examinations....Ch. 4.2 - Prob. 32ECh. 4.2 - Prob. 33ECh. 4.2 - Prob. 34ECh. 4.2 - Prob. 35ECh. 4.2 - Prob. 36ECh. 4.2 -
37. Resource Management The average weights of...Ch. 4.2 - Prob. 38ECh. 4.2 - Prob. 39ECh. 4.2 - Prob. 40ECh. 4.3 -
Find the transpose of each matrix.
1.
Ch. 4.3 - Prob. 2ECh. 4.3 - Prob. 3ECh. 4.3 - Find the transpose of each matrix. [...Ch. 4.3 -
State the dual problem for each linear...Ch. 4.3 - Prob. 6ECh. 4.3 -
State the dual problem for each linear...Ch. 4.3 - Prob. 8ECh. 4.3 - Prob. 9ECh. 4.3 -
Use the simples method to solve.
10. Find y1 ≥...Ch. 4.3 -
Use the simplex method to solve.
11. Find y1 ≥...Ch. 4.3 -
Use the simplex method to solve.
12. Minimize w...Ch. 4.3 - Prob. 13ECh. 4.3 -
Use the simplex method to solve.
14. Minimize w =...Ch. 4.3 - Prob. 15ECh. 4.3 - Prob. 16ECh. 4.3 - Prob. 17ECh. 4.3 - Prob. 18ECh. 4.3 -
19. Production Costs A brewery produces regular...Ch. 4.3 - Supply Costs The chemistry department at a local...Ch. 4.3 - Prob. 21ECh. 4.3 - Prob. 22ECh. 4.3 - Prob. 23ECh. 4.3 -
24. Animal Food An animal food must provide at...Ch. 4.3 - Feed Costs Refer to Example 5 in this section on...Ch. 4.3 - Prob. 26ECh. 4.3 - Calorie Expenditure Maureen Rachford wants to...Ch. 4.3 -
28. Health Care Greg Conover takes vitamin...Ch. 4.3 - 29. Blending Nutrients A biologist must make a...Ch. 4.4 - Prob. 1ECh. 4.4 - Prob. 2ECh. 4.4 - Prob. 3ECh. 4.4 - Prob. 4ECh. 4.4 -
Convert each problem into a maximization...Ch. 4.4 - Prob. 6ECh. 4.4 - Prob. 7ECh. 4.4 - Prob. 8ECh. 4.4 - Prob. 9ECh. 4.4 - Prob. 10ECh. 4.4 - Use the simplex method to solve. Find x1 0, x2 0...Ch. 4.4 - Prob. 12ECh. 4.4 - Prob. 13ECh. 4.4 - Prob. 14ECh. 4.4 - Prob. 15ECh. 4.4 - Prob. 16ECh. 4.4 - Prob. 17ECh. 4.4 - Prob. 18ECh. 4.4 - Solve using artificial variables. Maximize w =...Ch. 4.4 - Prob. 20ECh. 4.4 - Prob. 21ECh. 4.4 - Prob. 22ECh. 4.4 - Prob. 23ECh. 4.4 - Prob. 24ECh. 4.4 - Prob. 25ECh. 4.4 - Prob. 26ECh. 4.4 - Prob. 27ECh. 4.4 - Blending Seed Topgrade Turf lawn seed mixture...Ch. 4.4 - Prob. 29ECh. 4.4 - Prob. 30ECh. 4.4 - 31. Blending Chemicals Natural Brand plant food is...Ch. 4.4 - Prob. 32ECh. 4.4 -
33. Calorie Expenditure Joe Vetere’s exercise...Ch. 4 - Suppose you plan to build a raised flower bed...Ch. 4 - For the list of standard paper roll widths given...Ch. 4 - Prob. 3EACh. 4 - For the computer solution of the cutting problem,...Ch. 4 - Prob. 5EACh. 4 - Prob. 6EACh. 4 - Suppose that of the original 33 cutting patterns,...Ch. 4 - Prob. 8EACh. 4 - Compare your two answers from Exercise 8 with each...Ch. 4 - Prob. 10EACh. 4 -
Determine whether each of the following...Ch. 4 - Prob. 2RECh. 4 -
Determine whether each of the following...Ch. 4 - Prob. 4RECh. 4 -
Determine whether each of the following...Ch. 4 - Prob. 6RECh. 4 - Prob. 7RECh. 4 - Prob. 8RECh. 4 - Prob. 9RECh. 4 - Determine whether each of the following statements...Ch. 4 - Determine whether each of the following statements...Ch. 4 - Prob. 12RECh. 4 - Prob. 13RECh. 4 - Prob. 14RECh. 4 - Prob. 15RECh. 4 -
Determine whether each of the following...Ch. 4 -
For each problem. (a) add slack variables or...Ch. 4 - For each problem, (a) add slack variables or...Ch. 4 -
For each problem, (a) add slack variables or...Ch. 4 - For each problem, (a) add slack variables or...Ch. 4 -
Use the simplex method to solve each maximization...Ch. 4 - Use the simplex method to solve each maximization...Ch. 4 -
Use the simplex method to solve each maximization...Ch. 4 - Use the simplex method to solve each maximization...Ch. 4 - Convert each problem into a maximization problem...Ch. 4 - Convert each problem into a maximization problem...Ch. 4 - Prob. 27RECh. 4 - Prob. 28RECh. 4 - Prob. 29RECh. 4 - Prob. 30RECh. 4 - Prob. 31RECh. 4 - Prob. 32RECh. 4 - Prob. 33RECh. 4 - Prob. 34RECh. 4 - Prob. 35RECh. 4 -
36. In Chapter 2 we wrote a system of It near...Ch. 4 - Prob. 37RECh. 4 - Prob. 38RECh. 4 - Prob. 39RECh. 4 - Prob. 40RECh. 4 - Prob. 41RECh. 4 - Prob. 42RECh. 4 - Prob. 43RECh. 4 - Prob. 44RECh. 4 - Prob. 45RECh. 4 - Prob. 46RECh. 4 - Prob. 47RE
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