Mathematics All Around (6th Edition)
6th Edition
ISBN: 9780134506470
Author: Pirnot
Publisher: PEARSON
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Chapter 14.CR, Problem 1CR
To determine
To construct:
The frequency table and a bar graph for the group of students to perform the activity for increasing cardiovascular fitness.
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Students have asked these similar questions
You manage a chemical company with 2 warehouses. The following quantities of
Important Chemical A have arrived from an international supplier at 3 different
ports:
Chemical Available (L)
Port 1
Port 2
Port 3
400
110
100
The following amounts of Important Chemical A are required at your warehouses:
Warehouse 1
Warehouse 2
Chemical Required (L)
380
230
The cost in £ to ship 1L of chemical from each port to each warehouse is as follows:
Warehouse 1 Warehouse 2
Port 1
£10
£45
Port 2
£20
£28
Port 3
£13
£11
(a) You want to know how to send these shipments as cheaply as possible. For-
mulate this as a linear program (you do not need to formulate it in standard
inequality form) indicating what each variable represents.
a) Suppose that we are carrying out the 1-phase simplex algorithm on a linear program in
standard inequality form (with 3 variables and 4 constraints) and suppose that we have
reached a point where we have obtained the following tableau. Apply one more pivot
operation, indicating the highlighted row and column and the row operations you carry
out. What can you conclude from your updated tableau?
x1 12 23
81
82
83
S4
$1
-20
1 1
0
0
0
3
82
3 0
-2
0
1
2
0
6
12
1
1
-3
0
0
1
0
2
84
-3 0
2
0
0
-1 1 4
2
-2
0 11
0
0
-4
0
-8
b) Solve the following linear program using the 2-phase simplex algorithm. You should give
the initial tableau and each further tableau produced during the execution of the
algorithm. If the program has an optimal solution, give this solution and state its
objective value. If it does not have an optimal solution, say why.
maximize 21 - - 2x2 + x3 - 4x4
subject to 2x1+x22x3x4≥ 1,
5x1+x2-x3-4 -1,
2x1+x2-x3-342,
1, 2, 3, 4 ≥0.
Suppose we have a linear program in standard equation form
maximize c'x
subject to Ax=b,
x≥ 0.
and suppose u, v, and w are all optimal solutions to this linear program.
(a) Prove that zu+v+w is an optimal solution.
(b) If you try to adapt your proof from part (a) to prove that that u+v+w
is an optimal solution, say exactly which part(s) of the proof go wrong.
(c) If you try to adapt your proof from part (a) to prove that u+v-w is an
optimal solution, say exactly which part(s) of the proof go wrong.
Chapter 14 Solutions
Mathematics All Around (6th Edition)
Ch. 14.1 - Sharpening Your Skills. In Exercises 1 and 2,...Ch. 14.1 - Sharpening Your Skills. In Exercises 1 and 2,...Ch. 14.1 - Sharpening Your Skills. In Exercises 3 and 4,...Ch. 14.1 - Sharpening Your Skills. In Exercises 3 and 4,...Ch. 14.1 - Sharpening Your Skills. In Exercises 5 and 6,...Ch. 14.1 - Sharpening Your Skills. In Exercises 5 and 6,...Ch. 14.1 - Prob. 7ECh. 14.1 - Sharpening Your Skills. In Exercises 7 and 8,...Ch. 14.1 - Prob. 9ECh. 14.1 - Sharpening Your Skills. In Exercises 9 and 10,...
Ch. 14.1 - Prob. 11ECh. 14.1 - Prob. 12ECh. 14.1 - Applying What Youve Learned. Customers at...Ch. 14.1 - Applying What Youve Learned. Scheduling a rec...Ch. 14.1 - Applying What Youve Learned. Data similar to that...Ch. 14.1 - Applying What Youve Learned. Data similar to that...Ch. 14.1 - Comparing wage data. The following bar graphs...Ch. 14.1 - Applying What Youve Lerarned. Comparing wage data....Ch. 14.1 - Applying What Youve Learned. Comparing wage data....Ch. 14.1 - Applying What Youve Learned. Comparing wage data....Ch. 14.1 - Applying What Youve Learned. Comparing wage data....Ch. 14.1 - Prob. 22ECh. 14.1 - Prob. 23ECh. 14.1 - Prob. 24ECh. 14.1 - Prob. 25ECh. 14.1 - For Exercises 23 26, use the four graphs of the...Ch. 14.1 - Applying What Youve Learned. Comparing training...Ch. 14.1 - Applying What Youve Learned. Comparing weight-loss...Ch. 14.1 - Applying What Youve Learned. Super Bowl scores....Ch. 14.1 - Applying What Youve Learned. Law School Aptitude...Ch. 14.1 - In Exercises 31 34, first group the data using an...Ch. 14.1 - Applying What Youve Learned. In Exercises 31 34,...Ch. 14.1 - In Exercises 31 34, first group the data using an...Ch. 14.1 - Applying What Youve Learned. In Exercises 31 34,...Ch. 14.1 - Communicating Mathematics What is the difference...Ch. 14.1 - Communicating Mathematics If you are using a bar...Ch. 14.1 - Communicating Mathematics What is the difference...Ch. 14.1 - Communicating Mathematics What do you see as an...Ch. 14.1 - Challenge Yourself How might you present three...Ch. 14.1 - Challenge Yourself 42. The following table is an...Ch. 14.2 - Prob. 1ECh. 14.2 - Prob. 2ECh. 14.2 - Sharpening Your Skills Find the mean, median, and...Ch. 14.2 - Prob. 4ECh. 14.2 - Prob. 5ECh. 14.2 - Prob. 6ECh. 14.2 - Prob. 7ECh. 14.2 - Prob. 8ECh. 14.2 - Prob. 9ECh. 14.2 - Prob. 10ECh. 14.2 - Prob. 11ECh. 14.2 - Prob. 12ECh. 14.2 - Prob. 13ECh. 14.2 - Prob. 14ECh. 14.2 - Prob. 15ECh. 14.2 - Prob. 16ECh. 14.2 - In Exercises 1720, a give the five-number summary...Ch. 14.2 - Prob. 18ECh. 14.2 - In Exercises 1720, a give the five-number summary...Ch. 14.2 - In Exercises 1720, a give the five-number summary...Ch. 14.2 - In Exercises 2128, find the mean, median, and mode...Ch. 14.2 - In Exercises 2128, find the mean, median, and mode...Ch. 14.2 - In Exercises 2128, find the mean, median, and mode...Ch. 14.2 - In Exercises 2128, find the mean, median, and mode...Ch. 14.2 - In Exercises 2128, find the mean, median, and mode...Ch. 14.2 - In Exercises 2128, find the mean, median, and mode...Ch. 14.2 - In Exercises 2128, find the mean, median, and mode...Ch. 14.2 - In Exercises 2128, find the mean, median, and mode...Ch. 14.2 - Many colleges assign numerical points to grades as...Ch. 14.2 - Prob. 30ECh. 14.2 - Exam scores. Izzy had an 84 and an 86 on his first...Ch. 14.2 - Prob. 32ECh. 14.2 - Prob. 33ECh. 14.2 - Prob. 34ECh. 14.2 - Exam scores. Assume that in your History of Film...Ch. 14.2 - Prob. 36ECh. 14.2 - Prob. 37ECh. 14.2 - Prob. 38ECh. 14.2 - Prob. 39ECh. 14.2 - Example 6 Using Stem-and-Leaf Home Run Records...Ch. 14.2 - Prob. 41ECh. 14.2 - Prob. 42ECh. 14.2 - Prob. 43ECh. 14.2 - Prob. 44ECh. 14.2 - Prob. 45ECh. 14.2 - Prob. 46ECh. 14.2 - Prob. 47ECh. 14.2 - A college placement office has made a comparative...Ch. 14.2 - Prob. 49ECh. 14.2 - Prob. 50ECh. 14.2 - Give three separate real-life examples in which...Ch. 14.2 - Which measure of central tendency do you think is...Ch. 14.2 - Manipulating data. Choose some set of data...Ch. 14.2 - Analyzing misleading graphs. Find a graph in the...Ch. 14.2 - Prob. 55ECh. 14.2 - Prob. 56ECh. 14.2 - Prob. 57ECh. 14.2 - Prob. 58ECh. 14.2 - Prob. 59ECh. 14.2 - Prob. 60ECh. 14.2 - Prob. 61ECh. 14.2 - Prob. 62ECh. 14.2 - Prob. 63ECh. 14.2 - Prob. 64ECh. 14.2 - Prob. 65ECh. 14.3 - Sharpening Your Skills Find the range, mean, and...Ch. 14.3 - Sharpening Your Skills Find the range, mean, and...Ch. 14.3 - Sharpening Your Skills Find the range, mean, and...Ch. 14.3 - Sharpening Your Skills Find the range, mean, and...Ch. 14.3 - Sharpening Your Skills Find the range, mean, and...Ch. 14.3 - Sharpening Your Skills Find the range, mean, and...Ch. 14.3 - Sharpening Your Skills Find the range, mean, and...Ch. 14.3 - Sharpening Your Skills Find the range, mean, and...Ch. 14.3 - Prob. 9ECh. 14.3 - Prob. 10ECh. 14.3 - Prob. 11ECh. 14.3 - Prob. 12ECh. 14.3 - Prob. 13ECh. 14.3 - Prob. 14ECh. 14.3 - Prob. 15ECh. 14.3 - Prob. 16ECh. 14.3 - Prob. 17ECh. 14.3 - Prob. 18ECh. 14.3 - Prob. 19ECh. 14.3 - Applying What Youve Learned Summarizing age data....Ch. 14.3 - Prob. 21ECh. 14.3 - Prob. 22ECh. 14.3 - Prob. 23ECh. 14.3 - Prob. 24ECh. 14.3 - Prob. 25ECh. 14.3 - Prob. 26ECh. 14.3 - Prob. 27ECh. 14.3 - Prob. 28ECh. 14.3 - Prob. 29ECh. 14.3 - Prob. 30ECh. 14.3 - In Exercises 31 and 32, we present information on...Ch. 14.3 - In Exercises 31 and 32, we present information on...Ch. 14.3 - Human resources. As the manager of the human...Ch. 14.3 - Prob. 34ECh. 14.3 - Prob. 35ECh. 14.3 - Prob. 36ECh. 14.3 - Prob. 37ECh. 14.3 - Prob. 38ECh. 14.3 - Laptop batteries. A particular brand of laptop was...Ch. 14.3 - Study times. A group of students were sampled with...Ch. 14.3 - Prob. 41ECh. 14.3 - Prob. 42ECh. 14.3 - Prob. 43ECh. 14.3 - Use the following graphs for Exercise 44 a. Which...Ch. 14.3 - Prob. 45ECh. 14.3 - Prob. 46ECh. 14.3 - Prob. 47ECh. 14.3 - Prob. 48ECh. 14.4 - Assume that the distribution in Exercises 1 6 has...Ch. 14.4 - Assume that the distribution in Exercises 1 6 has...Ch. 14.4 - Assume that the distribution in Exercises 1 6 has...Ch. 14.4 - Assume that the distribution in Exercises 1 6 has...Ch. 14.4 - Assume that the distribution in Exercises 1 6 has...Ch. 14.4 - Assume that the distribution in Exercises 1 6 has...Ch. 14.4 - Assume that the distribution in Exercises 7 12...Ch. 14.4 - Assume that the distribution in Exercises 7 12...Ch. 14.4 - Assume that the distribution in Exercises 7 12...Ch. 14.4 - Assume that the distribution in Exercises 7 12...Ch. 14.4 - Assume that the distribution in Exercises 7 12...Ch. 14.4 - Assume that the distribution in Exercises 7 12...Ch. 14.4 - Use the following graph of the standard normal...Ch. 14.4 - Use the following graph of the standard normal...Ch. 14.4 - Use Table 14.19 to find the percent of the area...Ch. 14.4 - Use Table 14.19 to find the percent of the area...Ch. 14.4 - Use Table 14.19 to find the percent of the area...Ch. 14.4 - Prob. 18ECh. 14.4 - Prob. 19ECh. 14.4 - Prob. 20ECh. 14.4 - Prob. 21ECh. 14.4 - Prob. 22ECh. 14.4 - Use Table 14.19 to find the percent of the area...Ch. 14.4 - Prob. 24ECh. 14.4 - Use Table 14.19 to find the percent of the area...Ch. 14.4 - Use Table 14.19 to find the percent of the area...Ch. 14.4 - Use Table 14.19 to find the percent of the area...Ch. 14.4 - Prob. 28ECh. 14.4 - Use Table 14.19 to find the percent of the area...Ch. 14.4 - Prob. 30ECh. 14.4 - Use Table 14.19 to find the percent of the area...Ch. 14.4 - Prob. 32ECh. 14.4 - Use Table 14.19 to find the percent of the area...Ch. 14.4 - Prob. 34ECh. 14.4 - Prob. 35ECh. 14.4 - In Exercises 35 - 40, we give you a mean, a...Ch. 14.4 - Prob. 37ECh. 14.4 - Prob. 38ECh. 14.4 - Prob. 39ECh. 14.4 - Prob. 40ECh. 14.4 - Prob. 41ECh. 14.4 - In Exercises 41 - 46, we give you a mean, a...Ch. 14.4 - Prob. 43ECh. 14.4 - Prob. 44ECh. 14.4 - Prob. 45ECh. 14.4 - Prob. 46ECh. 14.4 - Prob. 47ECh. 14.4 - Prob. 48ECh. 14.4 - Prob. 49ECh. 14.4 - Prob. 50ECh. 14.4 - Prob. 51ECh. 14.4 - Prob. 52ECh. 14.4 - Prob. 53ECh. 14.4 - Prob. 54ECh. 14.4 - Prob. 55ECh. 14.4 - Prob. 56ECh. 14.4 - Prob. 57ECh. 14.4 - Prob. 58ECh. 14.4 - Prob. 59ECh. 14.4 - Prob. 60ECh. 14.4 - Prob. 61ECh. 14.4 - Prob. 62ECh. 14.4 - Prob. 63ECh. 14.4 - Weight lifting.In a power lifting competition the...Ch. 14.4 - Strength of cables.A certain type of cable has a...Ch. 14.4 - Prob. 66ECh. 14.4 - Prob. 67ECh. 14.4 - Prob. 68ECh. 14.4 - Prob. 69ECh. 14.4 - Prob. 70ECh. 14.4 - Prob. 71ECh. 14.4 - Prob. 72ECh. 14.4 - Prob. 73ECh. 14.4 - Prob. 74ECh. 14.4 - Analyzing the SATs. Assume that the math SAT...Ch. 14.4 - Prob. 76ECh. 14.4 - Prob. 77ECh. 14.4 - Prob. 78ECh. 14.4 - Prob. 79ECh. 14.4 - Prob. 80ECh. 14.4 - Prob. 81ECh. 14.4 - Prob. 82ECh. 14.4 - Prob. 83ECh. 14.4 - Prob. 84ECh. 14.4 - Prob. 85ECh. 14.4 - Prob. 86ECh. 14.4 - If a distribution has a mean of 40 and a standard...Ch. 14.4 - Prob. 88ECh. 14.4 - Prob. 89ECh. 14.4 - Prob. 90ECh. 14.5 - In Exercises 1 and 2, state what kind of...Ch. 14.5 - In Exercises 1 and 2, state what kind of...Ch. 14.5 - For Exercises 3 6, do the following: a. Plot the...Ch. 14.5 - Prob. 4ECh. 14.5 - Prob. 5ECh. 14.5 - Prob. 6ECh. 14.5 - Prob. 7ECh. 14.5 - Prob. 8ECh. 14.5 - Prob. 9ECh. 14.5 - Prob. 10ECh. 14.5 - Prob. 11ECh. 14.5 - Prob. 12ECh. 14.5 - In Exercises 11 14, find the line of best fit for...Ch. 14.5 - Prob. 14ECh. 14.5 - Prob. 15ECh. 14.5 - Prob. 16ECh. 14.5 - Prob. 17ECh. 14.5 - Prob. 18ECh. 14.5 - In Exercises 19 22, find the line of best fit for...Ch. 14.5 - In Exercises 19 22, find the line of best fit for...Ch. 14.5 - In Exercises 19 22, find the line of best fit for...Ch. 14.5 - In Exercises 19 22, find the line of best fit for...Ch. 14.5 - In Example 3, we found the absolute value of the...Ch. 14.5 - Prob. 24ECh. 14.5 - Prob. 25ECh. 14.5 - Prob. 26ECh. 14.5 - Prob. 27ECh. 14.CR - Prob. 1CRCh. 14.CR - Prob. 2CRCh. 14.CR - Prob. 3CRCh. 14.CR - Prob. 4CRCh. 14.CR - The lists represent the ages of actors M and...Ch. 14.CR - Prob. 6CRCh. 14.CR - Prob. 7CRCh. 14.CR - Prob. 8CRCh. 14.CR - Prob. 9CRCh. 14.CR - Prob. 10CRCh. 14.CR - Prob. 11CRCh. 14.CR - Prob. 12CRCh. 14.CR - Prob. 13CRCh. 14.CR - Prob. 14CRCh. 14.CR - Prob. 15CRCh. 14.CR - Prob. 16CRCh. 14.CR - Prob. 17CRCh. 14.CR - State what kind of correlation, if any, is...Ch. 14.CR - Prob. 19CRCh. 14.CT - Prob. 1CTCh. 14.CT - Prob. 2CTCh. 14.CT - Prob. 3CTCh. 14.CT - Prob. 4CTCh. 14.CT - Prob. 5CTCh. 14.CT - Prob. 6CTCh. 14.CT - Prob. 7CTCh. 14.CT - Prob. 8CTCh. 14.CT - Prob. 9CTCh. 14.CT - Prob. 10CTCh. 14.CT - Prob. 11CTCh. 14.CT - Prob. 12CTCh. 14.CT - Prob. 13CTCh. 14.CT - Prob. 14CTCh. 14.CT - Prob. 15CTCh. 14.CT - Prob. 16CTCh. 14.CT - Prob. 17CTCh. 14.CT - Prob. 18CT
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