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COMAP - For All Practical Purposes - 10/e (Homework)

James Finch

Math - Developmental, section A, Fall 2019

Instructor: Dr. Friendly

Current Score : 10 / 53

Due : Monday, December 30, 2030 23:59 EST

Last Saved : n/a Saving...  ()

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Question
Points
1 2 3 4 5 6 7 8 9
5/5 1/7 –/3 4/6 –/2 –/5 –/7 –/13 –/5
Total
10/53 (18.9%)

  • Instructions

    For All Practical Purposes 10th edition, by the Consortium for Mathematics and Its Applications, published by W. H. Freeman, remains the leading textbook for turning liberal arts students into skilled math users and consumers. It uses both contemporary and classic examples to help students appreciate the use of math in their everyday lives. The WebAssign component for this title includes links to appropriate sections of the eBook (not shown) along with extensive instructor and student textbook resources.

    Question 1 features three different types of answers: numerical, multiple choice, and multiple select.

    Question 2 utilizes special grading so a student can invent an algorithm different from the given information for finding TSP solutions.

    Question 3 utilizes special grading so a student can enter the arbitrary solutions as a separated list of answers in indicated format.

    Question 4 features the WebAssign graphing tool to graph a pair of equations in the same rectangular coordinate system.

    Question 5 has a student choose the appropriate graph from a selection of multiple choice graphs, in addition to finding an optimal solution.

    Questions 6 and 9 give the student an opportunity to use mathematics in a real-world application.

    Question 7 showcases grading of finding constraint inequalities and the profit formula.

    Question 8 requires the student to fill in empty cells of a Stem and Leaf Plot and summarize mean and median values. This demo assignment allows many submissions and allows you to try another version of the same question for practice wherever the problem has randomized values.

Assignment Submission

For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer.

Assignment Scoring

Your last submission is used for your score.

1. 5/5 points  |  Previous Answers FAPP10 1.4.054. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5
1/1 1/1 1/1 1/1 1/1
1/100 1/100 1/100 1/100 2/100
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5/5
 
Consider the following graph.
WebAssign Plot
(a)
Find the cheapest route in the accompanying graph, where one starts at vertex A, finishes at vertex A, and traverses each edge at least once. The cost of a route is computed by summing the numbers along the edges that one uses each time an edge is traversed. What is the cost of the cheapest route?
Correct: Your answer is correct. seenKey

61
(b)
How many edges are repeated in the minimal-cost route?
Correct: Your answer is correct. seenKey

3
(c)
What is the implication of this example for the relation between finding good eulerizations of graphs and the problem of finding cheap routes that start and end at the same vertex and traverse each edge at least once?
     Incorrect: Your answer is incorrect.
(d)
The edge with cost 23 in the diagram is not physically longer than other edges with lower costs attached to them. Why might it make sense in an urban setting to assign two stretches of street of similar length very different "costs" for traversing them?
     Correct: Your answer is correct.
(e)
What are some different meanings that "weights" (for example, traffic volume) potentially assigned to edges in a graph might have in an urban setting? (Select all that apply.)
Incorrect: Your answer is incorrect.

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2. 1/7 points  |  Previous Answers FAPP10 2.3.048. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7
1/1 –/1 0/1 –/1 0/1 0/1 –/1
1/100 0/100 1/100 0/100 1/100 1/100 0/100
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1/7
 
Consider the following graphs.
(a)
(b)
(a)
For the two complete graphs above, find the costs of the nearest-neighbor tour starting at C and of the tour generated by the sorted-edges algorithm.
graph (a) graph (b)
nearest-neighbor Correct: Your answer is correct. seenKey

236
sorted-edges Incorrect: Your answer is incorrect. seenKey

236
(b)
How many Hamiltonian circuits would have to be examined to find a shortest route for part (a) by the brute force method?
graph (a) Incorrect: Your answer is incorrect. seenKey

12

 circuits graph (b) Incorrect: Your answer is incorrect. seenKey

60

 circuits
(c)
Invent an algorithm different from the sorted-edges and nearest-neighbor algorithms that is easy to apply for finding TSP solutions.

This answer has not been graded yet.

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3. –/3 points FAPP10 2.5.079. My Notes
Question Part
Points
Submissions Used
1 2 3
–/1 –/1 –/1
0/100 0/100 0/100
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–/3
 
In the accompanying order-requirement digraph, determine which tasks, if shortened, would reduce the earliest completion time. (Enter the task a as Ta. Enter your answers as a comma-separated list.)
Find the earliest completion time if task
T5
 is reduced to time length 7.
What is the new critical path? (Enter your path in the form TaTbTc...)
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4. 4/6 points  |  Previous Answers FAPP10 4.1.007. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6
1/1 1/1 0/1 1/1 –/1 1/1
1/100 1/100 1/100 1/100 0/100 1/100
Total
4/6
 
(a)
Graph both lines on the same axes. Put a dot where the lines intersect.
6x + 3y = 21
 and
x = 0
No Solution
Help
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Clear Graph
Delete Layer
Fill
Show Key

Graph LayersToggle Open/Closed

Submission Data

Correct: Your answer is correct.
seenKey

line: 3*y+6*x=21; line: x=0; point: (0,7)
Use algebra to find the x- and y-coordinates of the point of intersection.
(x, y) = 
0,7
Correct: Your answer is correct. webMathematica generated answer key
(b)
Graph both lines on the same axes. Put a dot where the lines intersect.
4x + 3y = 36
 and
y = −4
No Solution
Help
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Clear Graph
Delete Layer
Fill
Show Key

Graph LayersToggle Open/Closed

Submission Data

Incorrect: Your answer is incorrect.
seenKey

line: 3*y+4*x=36; line: y=-4; point: (12,-4)
Use algebra to find the x- and y-coordinates of the point of intersection.
(x, y) = 
12,−4
Correct: Your answer is correct. webMathematica generated answer key
(c)
Graph both lines on the same axes. Put a dot where the lines intersect.
4x + 3y = 36
 and
x = 3
No Solution
Help
-14
-12
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Clear Graph
Delete Layer
Fill

Graph LayersToggle Open/Closed

  • After you add an object to the graph you can use Graph Layers to view and edit its properties.
Use algebra to find the x- and y-coordinates of the point of intersection.
(x, y) = 
3,8
Correct: Your answer is correct. webMathematica generated answer key
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5. –/2 points FAPP10 4.4.038. My Notes
Question Part
Points
Submissions Used
1 2
–/1 –/1
0/100 0/100
Total
–/2
 
Given profit
P = 21x + 11y
 subject to the constraints
x ≥ 0,
y ≥ 0,
8x + 5y ≤ 14,
 do the following.
(a)
Graph the feasible region.

(b)
Determine a corner point where there is an optimal solution. (Warning: The corner point where the optimal solution occurs may not have integer values for both x and y.)
Corner Point (x, y) =
 
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6. –/5 points FAPP10 4.4.046. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5
–/1 –/1 –/1 –/1 –/1
0/100 0/100 0/100 0/100 0/100
Total
–/5
 
This exercise requires finding the point of intersection of two lines, each corresponding to a resource constraint.
The firm WebsAreUs creates and maintains web sites for client companies. There are two types of web sites: "hot" sites change their layout frequently but keep their content for long times; "cool" sites keep their layout for a while but frequently change their content. Maintaining a hot site requires 1.5 hr of layout time and 1 hr for content changes. Maintaining a cool site requires 1 hr of layout time and 2 hr for content changes. Every day, WebsAreUs has available 13 hr for layout changes and 18 hr for content changes. Net profit is $50 for a set of changes on a hot site and $250 for a set of changes on a cool site.
To maximize profit, how many of each type of site should WebsAreUs maintain daily?
hot cool
If the company must maintain at least two hot and six cool sites daily, what is the optimal policy?
hot cool This additional constraint the maximum profit.
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7. –/7 points FAPP10 4.4.052. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7
–/1 –/1 –/1 –/1 –/1 –/1 –/1
0/100 0/100 0/100 0/100 0/100 0/100 0/100
Total
–/7
 
There are more than two products in this problem. Although you cannot solve this problem using the two-dimensional graphical method, you can write the minimum and resource constraint inequalities and the profit formula.
A toy company makes three types of toys, each of which must be processed by three machines: a shaper, a smoother, and a painter. Each Toy A requires 1 hr in the shaper, 2 hr in the smoother, and 1 hr in the painter, and brings in a $3 profit. Each Toy B requires 2 hr in the shaper, 1 hr in the smoother, and 3 hr in the painter, and brings in a $6 profit. Each Toy C requires 3 hr in the shaper, 2 hr in the smoother, and 1 hr in the painter, and brings in a $8 profit. The shaper can work at most 50 hr per week, the smoother 40 hr, and the painter 60 hr. What production policy would maximize the toy company's profit?
Constraints
A
≥
 B
≥
 C
≥
shaper
smoother
painter
profit P =
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8. –/13 points FAPP10 5.4.018. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8 9 10 11 12 13
–/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1
0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100
Total
–/13
 
Here are a baseball player's home run totals for each year of his career.
14 27 23 18 30 23 34 45
37 31 45 40 39 34 45 70
46 45 46 6 24 27
(a)
Make a stemplot of the data. Are there any outliers? (Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.)
Stem Leaf
0
1
2
3
4
5
6
7
(b)
Find the player's career mean and median number of home runs. (Round your answers to one decimal place.)
mean median
What is his career mean and median when you drop his best season of 70? (Round your answers to one decimal place.)
mean median
What general fact about the mean and median does your result illustrate?
    
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9. –/5 points FAPP10 12.3.025. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5
–/1 –/1 –/1 –/1 –/1
0/100 0/100 0/100 0/100 0/100
Total
–/5
 
Suppose that the continuous distribution of voters' ideal points is the bent solid line in the accompanying figure. (Note: This is a continuous distribution because the triangle under the bent solid line has area 1.) Assume that A's policy position is 3 on the left-right continuum; it is denoted by the dashed line.
WebAssign Plot
If B announces a policy position at 0.5 which candidate wins the election?
    
If B announces a policy position at 2 which candidate wins the election?
    
If B announces a policy position at 3.5 which candidate wins the election?
    
What is the median position?
Describe which voters vote for B if B announces the median. (Enter your answer using interval notation.)
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