You can use a calculator to do numerical calculations. No graphing calculator is allowed. Please DO NOT USE ANY COMPUTER SOFTWARE to solve the problems.

 

 

 

 

 

1. (a) What is an assignment problem? Briefly discuss the decision variables, the objective function and constraint requirements in an assignment problem. Give a real world example of the assignment problem.

 

 

 

(b) What is a diet problem? Briefly discuss the objective function and constraint requirements in a diet problem. Give a real world example of a diet problem.

 

 

 

(c) What are the differences between QM for Windows and Excel when solving a linear programming problem? Which one you like better? Why?

 

 

 

(d) What are the dual prices? In what range are they valid? Why are they useful in making recommendations to the decision maker? Give a real world example.

 

 

 

Answer Questions 2 and 3 based on the following LP problem.

 

 

 

Let     P1 = number of Product 1 to be produced

 

P2 = number of Product 2 to be produced

 

P3 = number of Product 3 to be produced

 

P4 = number of Product 4 to be produced

 

 

 

Maximize 80P1 + 100P2 + 120P3 + 70P4        Total profit

 

Subject to

 

10P1 + 12P2 + 10P3 + 8P4 ≤ 3200       Production budget constraint

 

4P1 + 3P2 + 2P3 + 3P4 ≤ 1000       Labor hours constraint

 

5P1 + 4P2 + 3P3 + 3P4 ≤ 1200       Material constraint

 

P1 > 100         Minimum quantity needed for Product 1 constraint

 

And P1, P2, P3, P4 ≥ 0             Non-negativity constraints

 

 

 

The QM for Windows output for this problem is given below.

 

 

 

Linear Programming Results:

 

Variable           Status   Value

 

P1        Basic    100

 

P2        NONBasic       0

 

P3        Basic    220

 

P4        NONBasic       0

 

slack 1NONBasic       0

 

slack 2Basic    160

 

slack 3Basic    40

 

surplus 4          NONBasic       0

 

Optimal Value (Z)        34400

 

 

 

Original problem w/answers:

 

P1        P2         P3         P4          RHS        Dual

 

Maximize              80       100       120        70

 

Constraint 1          10         12         10         8   <=    3200         12

 

Constraint 2           4           3          2          3   <=    1000          0

 

Constraint 3           5           4          3          3   <=    1200          0

 

Constraint 4          1            0          0          0   >=      100       -40

 

Solution->         100            0      220          0   Optimal Z->    34400

 

 

 

Ranging Results:

 

Variable           Value   Reduced Cost  Original Val     Lower Bound   Upper Bound

 

P1        100      0          80        -Infinity           120

 

P2        0          44        100      -Infinity           144

 

P3        220      0          120      87.5     Infinity

 

P4        0          26        70        -Infinity           96

 

 

 

Constraint        Dual Value      Slack/Surplus   Original Val     Lower Bound   Upper Bound

 

Constraint 1     12        0          3200    1000    3333.333

 

Constraint 2     0          160      1000    840      Infinity

 

Constraint 3     0          40        1200    1160    Infinity

 

Constraint 4     -40       0          100      0          120

 

 

 

 

 

2. (a) Determine the optimal solution  and optimal value and interpret their meanings.

 

(b) Determine the slack (or surplus) value for each constraint and interpret its meaning.

 

 

 

 

 

3. (a) What are the ranges of optimality for the profit of Product 1, Product 2, Product 3, and Product 4?

 

(b) Find the dual prices of the four constraints and interpret their meanings. What are the ranges in which each of these dual prices is valid?

 

(c) If the profit contribution of Product 2 changes from $100 per unit to $130 per unit, what will be the optimal solution? What will be the new total profit? (Note: Answer this question by using the ranging results given above).

 

(d) Which resource should be obtained in larger quantity to increase the profit most? (Note: Answer this question using the ranging results given above.).

 

 

 

 

 

4. The Portfolio Manager of Charm City Pension Planners, Inc., has been asked to invest $1,000,000 of a large pension fund. The management of the company has identified five mutual funds as possible investment options. The details of these five mutual funds are given below:

 

 

 

                                                                  Mutual Fund

 

1           2           3            4             5

 

Annual return (in dollars)     12%       10%      8.5%       10%      11%

 

Risk amount (in dollars)       9.8%       8%      7.2%       7.1%     7.3%

 

 

 

To control the risk, the management of the company has specified that the total risk amount cannot exceed $200,000. In addition, the management wants to invest at least $150,000 in mutual fund 2 and at least $125,000 in mutual fund 3.

 

 

 

With these restrictions, how much money should the portfolio manager of the company invest in each mutual fund so as to maximize the total annual return?

 

 

 

(a) Define the decision variables.

 

(b) Determine the objective function. What does it represent?

 

(c) Determine all the constraints. Briefly describe what each constraint represents.

 

 

 

Note: Do NOT solve the problem after formulating.

 

 

 

 

5. A charity wants to contact people to collect donations. A person can be contacted morning or evening, by phone, or door-to-door. The average donation resulting from each type of contact is given below:

 

 

 

Phone          Door-to-Door

 

____________________________________

 

Morning           $35                    $60

 

Evening            $40                    $70

 

 

 

The Charity has 150 volunteer hours in the morning and 120 volunteer hours in the evening. Each phone contact takes 6 minutes and each door-to-door contact takes 15 minutes to conduct. The Charity wants to have at least 550 phone and at least 400 door-to-door contacts.

 

 

 

Formulate a linear programming model that meets these restrictions and maximizes the total average donations by determining

 

 

 

(a) The decision variables.

 

(b) Determine the objective function. What does it represent?

 

(c) Determine all the constraints. Briefly describe what each constraint represents.

 

 

 

Note: Do NOT solve the problem after formulating

 

 

 

6. The Charm City Truck Rental Inc. has accumulated extra trucks at three of its truck leasing outlets, as shown in the following table:

 

 

 

Leasing Outlet            Extra Trucks

 

1. Atlanta               70

 

2. St. Louis          115

 

3. Greensboro        60

 

 

 

The firm also has three outlets with shortages of rental trucks, as follows:

 

 

 

Leasing Outlet            Truck Shortage

 

A. New Orleans          80

 

B. Cincinnati             50

 

C. Baltimore             45

 

 

 

The firm wants to transfer trucks from those outlets with extras to those with shortages at the minimum total cost. The following costs of transporting these trucks from city to city have been determined:

 

 

 

To (cost in dollars)          

 

From      A      B         C

 

1            75      80        45

 

2          115      50        55

 

3          100      60        40

 

 

 

For this transportation problem:

 

 

 

(a) Define the decision variables.

 

(b) Determine the objective function. What does it represent?

 

(c) Determine all the constraints. Briefly describe what each constraint represents.

Write a 1000 word book review on Kidd’s The Invention of Wings. 

Briefly define emotional contagion. Think about situations in which you have experienced or observed the phenomenon of emotional contagion. How might this phenomenon affect individuals in their work or careers, both positively or negatively? What suggestions might help individuals who work closely with others to avoid initiating or being affected negatively by emotional contagion?

Textbook
Baron,r.a.,& branscombe,n.r.(2012 social psychology 13th ed boston:pearson
ISBN-13;978-0205205585

Should psychiatrists have a monopoly on the treatment of mental illness? Use peer reviewed sources to support that, no, other professionals such as psychologists, nurses, therapists, social workers and occupational workers play essential roles in the field of mental health care. All are necessary to work cohesively together.

Should same sex marriage be a states’ rights issue?

In Pride and Prejudice, Elizabeth mentions that her sister, Jane, and Jane’s beau, Mr. Bingley, “both like Vingt-un better than Commerce” (23). A footnote informs us that, while both Vingt-un and Commerce are card games, “Vingt-un involves more risk and requires less strategic attention to others’ moves” (419). What might this shared preference signal about Jane and Bingley’s relationship, over and against the other pairings in the novel? Keep in mind that in the tightly regulated “marriage market” of Austen’s society the stakes for women were extremely high. Analyze, and then develop an argument about how Austen, as a novelist, manages the varying levels of risk her female characters take on as they negotiate the partnerships that will determine their future security.

This paper requires an outline to go along with it. 1.1 Outline Write a thesis statement that is one to two (1-2) sentences long in which you: a.State your thesis on how industrialization after the Civil War influenced U.S. society, economy, and politics. Justify your response. For the first part of this assignment you will create a thesis statement. A thesis statement is usually a single sentence somewhere in your first paragraph that presents your main idea to the reader. The body of the essay organizes the material you gather and present in support of your main idea. Keep in mind that a thesis is an interpretation of a question or subject, not the subject itself. (Note: Please consult the Purdue OWL Website with tips on how to construct a proper thesis; the website can be found at: https://owl.english.purdue.edu/owl/resource/545/01/ Part 2: For the next part of this assignment you will create an outline of the main points you want to address in this paper. This outline will serve as the basis for your Assignment 1.2 Final Draft. (Note: Please use the Purdue Owl Website to assist you with this assignment; this website can be accessed at: https://owl.english.purdue.edu/engagement/2/2/55/ 2.Write a one to two (1-2) page outline in which you: a.List three (3) major aspects of industrialization between 1865 and 1920. In your response, consider society, the economy, and politics. b.List five (5) specific groups that were affected by industrialization. Provide two (2) examples for each group describing how the group was affected. (Consider issues such as race, ethnicity, gender, child labor, etc.) c.List five (5) ways that industrialization affected the life of the average working American during this period. d.Use at least three (3) academic references besides or in addition to the textbook. Note: Wikipedia and other Websites do not qualify as academic resources. Your assignment must follow these formatting requirements: •Be typed, double spaced, using Times New Roman font (size 12), with one-inch margins on all sides; citations and references must follow APA or school-specific format. Check with your professor for any additional instructions. •Include a cover page containing the title of the assignment, the student’s name, the professor’s name, the course title, and the date. The cover page and the reference page are not included in the required assignment page length. The specific course learning outcomes associated with this assignment are: •Identify and discuss the different ways that the Civil War, Reconstruction, and Industrialization after the Civil War have shaped America’s history. •Summarize and discuss the ways that formal policies of government have influenced the direction of historical and social development in the United States. •Recognize the major turning points in American history since the Civil War. •Use technology and information resources to research issues in contemporary U.S. history. •Write clearly and concisely about contemporary U.S. history using proper writing mechanics. 1.2 paper After the Civil War, the United States became a much more industrialized society. Between 1865 and 1920, industrialization improved American life in many ways. However, industrialization also created problems for American society. Consider events that took place after the Civil War and discuss ways that industrialization affected the U.S. between 1865 and 1920. You have already developed a thesis statement and developed an outline in which you identify three main points relevant to your topic. Now you will develop the final paper in which you explore your main points in detail. Write a three to five (3-5) page paper in which you: 1.Introduce your paper with your previously crafted thesis statement. 2.Discuss three (3) major aspects of industrialization between 1865 and 1920. In your response, consider society, the economy, and politics. 3.Identify three (3) specific groups that were affected by industrialization and provide two examples for each group describing how the group was affected. (Consider issues such as race, ethnicity, gender, child labor, etc.) 4.Summarize how industrialization affected the life of the average working American during this period. Use specific examples and details. 5.Use at least three (3) academic references besides or in addition to the textbook. Note: Wikipedia and other Websites do not qualify as academic resources. Your assignment must follow these formatting requirements: •Be typed, double spaced, using Times New Roman font (size 12), with one-inch margins on all sides; citations and references must follow APA style or school-specific format. Check with your professor for any additional instructions. •Include a cover page containing the title of the assignment, the student’s name, the professor’s name, the course title, and the date. The cover page and the reference page are not included in the required assignment page length. The specific course learning outcomes associated with this assignment are: •Identify and discuss the different ways that the heritage of slavery, the Civil War, the Reconstruction, and segregation have shaped America’s history. •Summarize and discuss the ways that formal policies of government have influenced the direction of historical and social development in the United States. •Recognize the major turning points in American history since the Civil War. •Use technology and information resources to research issues in contemporary U.S. history. •Write clearly and concisely about contemporary U.S. history using proper writing mechanics

The following items will be assessed in particular: 1.In your own words, define “health behavior” and define “risk factors”. Be sure to cite a reference even though you used your own words. 2.Describe the Behavioral Risk Factor Surveillance System (BRFSS). 3.At the Behavioral Risk Factor Surveillance System’s Web page, click on the link for State Information. How are the BRFSS data used in your State? Be sure to tell me which State you are writing about. 4.Reflect upon ways you can address this health behavior through your role in your chosen health profession.

Instructions

As you prepare this and subsequent essays, please review sections on “Essay Grading” in Unit 1. You may also want to review various sections of your college composition course handbook that deal with organizing and composing effective essays. Your essay should present a clear, insightful central idea, should have a clear sense of order and logic, should be well developed with specific details to support your assertions, and should use effective language that is free of grammar, spelling, and punctuation errors. Avoid plot summaries and provide quotations from the text to support your ideas. Consult the Writing About World Literature by Karen Gocsik for writing instructions. Also, it is suggested that you spend ample time writing and revising your essay. How to format your paper: Typed/printed, double-spaced, 1″ margins. Change them in “Page Setup” on the “File” menu. Paragraphs indented 5 spaces at left; do not separate paragraphs by extra blank lines. Quotations of 10 words or less should be integrated into the text; longer quotations should be indented 5 spaces at left and right margins, single spaced, and set off from the text of the essay by a blank line before and after the quotation. Be sure to include verse numbers or line numbers Avoid citing college dictionaries, Wikipedia, or basic references such as the OED, Encyclopedia Britannica, etc. Instead, use the text, discussion postings, lesson notes, and any sources accessed from GALILEO for outside reference. Each essay should have a specific title – one that suggests what is the most interesting or important about what you have to say. It’s worth taking a little thought over the title, not only because it creates the first impression of your essay; coming up with a phrase which encapsulates your argument can help in focusing that argument. One popular strategy is to use a key phrase from the text followed by another phrase of clarification. Notes: All papers submitted in this class are reviewed via Turnitin.com, a proprietary software database that identifies unoriginal material in papers. Please review the syllabus statement regarding the penalty for plagiarism.Your instructor will provide you with additional information. Dates for essay submissions will be outlined in the course Calendar. Your Assignment: Write a 1500-2000 word paper that compares two or three literary works from different periods or cultures (at least one must be a work you have not written about before) in terms of: Their generic form and conventions as related to or even as outcomes of their social, religious and political milieus OR a demonstration of the historical development of the genre Their mythic contents and functions in their cultures’ mythology. Note: For the final paper, at least one work must be a work you have not written about before You will want to review while making your topic decision. Present your topic to your instructor for approval by the date indicated on the course calendar. Papers on unapproved topics will not be graded. You are not required to do research, but if you decide to do so, you must then include at least two sources on each literary work so that you do not simply repeat what someone else has concluded, and you must properly quote or paraphrase, including citations in MLA form. The following offer examples of the types of topics you might expect for the final paper. Very likely, neither of these examples will be topics you will be allowed to write on. Generic Topic Example The Classic of Poetry and Son-Jara both contain various types within the whole, and they were both composed or collected over a period of time. What seem to be the functions of the different types of poetry in Classic of Poetry and the praise poems, genealogies, narrative episodes and other genres within the epic of Son-Jara? What ideas are suggested about the emergence or existence of literary genres? Mythic Topic Example Monsters are a feature in myths, epics, and other literary works from all over the world. Compare and contrast the monsters in Gilgamesh, the Odyssey and the Ramayana. Explain what these non-human creatures represent in relation to the cultures of the narratives in which they appear and whether they have universal significance.