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Buy your Custom Essay-EG-260 Continuous Assessment 1


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 EG-260 Continuous Assessment 1

Warning: Failure to follow these instructions will result in zero mark for the entire assessment. These instructions are purposefully very detailed and highlight common mistakes that have been seen in the past. My goal is to make sure that you communicate your answers to this assessment in the correct manner so that I can assign you the correct marks. It is therefore crucial that you read, understand and follow these instructions.

 

Instructions:

  • This assessment must be solved and submitted individually. The submission deadline is:

 

23.59 on Thursday 9 March 2017

 

  • Use numerical values for the parameters corresponding to your student number from xls file available on blackboard.

 

 

  • Solve all of the questions in this assessment using the parameters that are assigned to your student number. Remember: Each answer that you will obtain WILL be a numerical value. When solving the questions, maintain highest possible decimal points. Your final answer should be rounded to 4 decimal places (done automatically in the xls file).

 

  • Download the empty answer file (xls) to your computer from the Blackboard page. This is the file where you will enter your answers to the questions. The only change that you should do to this file is to enter your answers and to save it! Do NOT rename this file. Do NOT change the file format, for example to .xlsx. Do NOT change the internal formatting of the file. Do NOT change or add new sheets to the file. Your task is to simply enter ONLY numerical values for your answers to this file and save it! Do not put units as they are already in the questions. Do NOT enter ANY non-numerical characters (such as “2*10^2”, “10e4”) or incomplete calculations such as “2×2” or “2*100” or “50/3 – 100”.

 

  • Submit the Excel file (xls) in Blackboard.

 

  • IN ADDITION to the xls file, you MUST submit a SINGLE file containing the supporting work. This file should show how you have solved the problems. This is the evidence that you obtained the numerical results yourself. You can type your solution in WORD or SCAN your handwritten work. Either way, submission should be a PDF file. Remember, this FILE NAME must be MySolution.pdf. Do NOT submit separate files for different parts of your solution. Avoid JPG, TIF or other image files if possible.

 

  • Numerical answers in both files must agree with each other. In case of any discrepancies, the answers in xls will be used for marking.

 

  • Unlike the final exam, no method marks is available for this assessment. You have to get correct numerical values and enter it correctly as described above. This is because, unlike the final exam, you have one full week to solve the two problems.

 

  • Please submit the two files ONLY once.


  • Question 1: An inverted pendulum oscillator of length L [m] and mass m [kg] is attached by springs. Two springs of stiffness values k1 and k2 [N/m] are arranged in parallel and series respectively as shown below:

 

Important: The values of L, m, k1 and k2 in SI units are given for your student number in the excel file CA1_Parameters.xls. Use an equivalent spring in deriving the equation of motion and consider the weight of the mass. Take gravitational acceleration constant as 9.8100 [m/s2]. All answers must be in numerical format and in SI units.

 

Case 1: springs in parallel                      Case 2: springs in series

  1. Calculate the equivalent spring stiffness for case 1 and enter the numerical value to the designated cell in the Excel file.                                     (5 Marks)
  2. Calculate the equivalent spring stiffness for case 2 and enter the numerical value to the designated cell in the Excel file.                                                               (5 Marks)
  3. Assuming the rotation is small, obtain the equation of motion. From this, calculate the natural frequency in rad/sec for case 1 and enter the numerical value to the designated cell in the Excel file.              (15 Marks)
  4. From the equation of motion, calculate the natural frequency in rad/sec for case 2 and enter the numerical value to the designated cell in the Excel file. (15 Marks)
  5. Assuming k2 = 2k1, obtain the value of k1 (in N/m) for the system to be stable for case 1 and enter the numerical value to the designated cell in the Excel file. (5 Marks)
  6. Assuming k2 = 2k1, obtain the value of k1 (in N/m) for the system to be stable for case 2 and enter the numerical value to the designated cell in the Excel file.      (5 Marks)

 

 


 

Question 2: A vibrating system consisting of a weight of W [N] and a spring stiffness of k [N/m] is viscously damped such that the ratio of any two consecutive amplitudes is 10 to y. Determine:

 

  1. Log decrement () and enter the numerical value to the designated cell in the Excel file.                        (10 Marks)
  2. Damping factor () and enter the numerical value to the designated cell in the Excel file.                   (10 Marks)
  3. Damped natural frequency () in (rad/sec) and enter the numerical value to the designated cell in the Excel file.    (15 Marks)
  4. Damping constant (c) and enter the numerical value to the designated cell in the Excel file.                (15 Marks)

 

Hint: The values of W, k, and y in SI units are given for your student number in the Excel file CA1_Parameters.xls. Take gravitational acceleration constant as 9.8100 [m/s2]. All answers must be in numerical format and in SI units.

 

Reminder: Failure to follow the instructions will result in zero marks even if you obtained correct answers! For the sake of fairness, no exceptions will be allowed. Unless you are ABSOLUTELY sure that your submission is according to the instructions, please do not upload it in the blackboard.

 

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Assignment help-FIN 415 Spring 2017 Homework Set 4


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FIN 415 Spring 2017 Homework Set 4

Please turn in page 3 only – Thanks!

Problem 1: Assume that the forward rate of a 1-Year long forward GBP is 𝐹1𝑈𝑆𝐷𝐺𝐵𝑃⁄=1.30. The amount of the contract is USD 250,000. What is the size of the contract?

Problem 2: The size of a 1-Year forward AUD (Australian dollars) is AUD 260,000 and the amount is USD 182,000. What is the 1-Year USD/AUD forward rate?

Problem 3: What is the profit/loss on a 1-Year long forward EUR at t=1 when 𝑋1𝑈𝑆𝐷𝐸𝑈𝑅⁄=1.11; 𝐹1𝑈𝑆𝐷𝐸𝑈𝑅⁄=1.22 and the size of the contract is EUR 350,000?

Problem 4: What is the size of a difference check on a 1-Year short forward GBP contract given that the size of the contract is GBP 500,000; the amount of the contract is USD 625,000; and 𝑋1𝑈𝑆𝐷𝐺𝐵𝑃⁄=1.30 ?

Problem 5: Assume that 𝑟𝐸𝑈𝑅=7% and 𝑟𝑈𝑆𝐷=4%. What is the 1-Year synthetic forward rate, given that 𝑋0𝑈𝑆𝐷𝐸𝑈𝑅⁄=1.16?

Problem 6: Today’s GBP/USD spot rate is, 𝑋0𝑈𝑆𝐷𝐺𝐵𝑃⁄=1.28. Assume that 𝑟𝐺𝐵𝑃=6% and 𝑟𝑈𝑆𝐷=4%, if the 1-Year USD/GBP forward rate is 𝐹1𝑈𝑆𝐷𝐺𝐵𝑃⁄=1.28, according to the Covered Interest Rate parity (CIRP), is the GBP underpriced/overpriced in the actual forward contract?
2
Problem 7: Based on the information in Problem 6, assuming that you can borrow 500,000 units in the synthetic forward position at t=0, what would your profit be from CIRP arbitrage (in USD)?

Problem 8: Assume that 𝑟𝐸𝑈𝑅=10%, 𝑟𝑈𝑆𝐷=3% and 𝑋0𝑈𝑆𝐷𝐸𝑈𝑅⁄=1.32. You want a long forward position in EUR 210,000 1-Year forward, i.e. receive EUR one year in the future. Your banker quotes you the following USD/EUR forward rate: 𝐹1𝑈𝑆𝐷𝐸𝑈𝑅⁄=1.22. Will you enter the actual forward contract or set up a synthetic forward position?

Problem 9: Assume you want a short position in AUD in a 1-Year USD/AUD contract. You calculate the synthetic forward at 𝐹𝑌1𝑈𝑆𝐷𝐴𝑈𝐷⁄=0.80 and your banker quotes you 𝐹1𝑈𝑆𝐷𝐴𝑈𝐷⁄=0.82. Do you choose the actual forward contract or the synthetic forward?
Problem 10: Compute the mark-to-market value of the following short forward NZD (New Zealand Dollar) contract. The size of the short position is NZD 450,000 and the forward rate is 𝐹𝑁𝑈𝑆𝐷𝑁𝑍𝐷⁄=0.66; the current spot rate (at time of valuation) 𝑋0𝑈𝑆𝐷𝑁𝑍𝐷⁄=0.64 . The NZD and USD interest rates are: 𝑟𝑁𝑍𝐷=9% and 𝑟𝑈𝑆𝐷=3%; assume the contract matures in two years from now (so at t=2).
Bonus Problem: Which of the following two statements is correct?
S1: According to CIRP, the spot price of the high interest rate currency is expected to appreciate.
S2: According to CIRP, forward rates and synthetic forward rates are the same.
a) S1 is true but S2 is false
b) S2 is true but S1 is false
c) Both statements are true
d) Both statements are false
3
FIN 415 Homework 4 Spring 2017 Name:____________________________________
Problem 1:
Problem 2:
Problem 3:
Problem 4:
Problem 5:
Problem 6:
Problem 7:
Problem 8:
Problem 9:
Problem 10:
Bonus Question:

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Homework help-Econ 4400, Elementary Econometrics


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HOMEWORK4

Econ 4400, Elementary Econometrics

Directions: Please follow the instructions closely. Questions 1-10 are worth 9 points each. Question 11 is worth 10 points.

Due: All problem sets have to be turned in at the beginning of the class. Due Dates: March 2

Table 1 includes regression results using the NLSY 97 data set. The omitted racial group is ”non-black/ non-Hispanic”. The omitted census region is ”West”. The omitted favorite ice cream flavor is Chocolate.

Using the regression results in Table 1 perform each of the following tests. Use 0.05 significance level for every problem unless otherwise noted. You should write both the null and alternative hypotheses, calculate the necessary statistics, find correct critical values, and make the correct conclusion

  1. Use a t-test to test if education has a statistically significant(2-sided) effect on income in column 1.
  2. Use a t-test to test the null hypothesis that black workers make more than nonblack/non-Hispanic, all else equal.
  3. Find confidence intervals for the coefficient on education in column 1 and column

 

  1. Use the SSR version of the F-test to test the joint significance of the regional variables. (You can ignore the e + 12)
  2. Use the R2 version of the F-test to test the joint significance of the regional variables.
  3. Why does the coefficient on education change in each regression? Why would it be so much different in columns 1 and 3?
  4. Column 4 includes favorite ice cream flavor. Use an F-test to show that they should not be included.
  5. Typically there are stars to denote p-values on regression results. If 1,2, or 3 stars were added for p-values< 0.10, < 0.05, and < 0.01 respectively. How many stars would go on the coefficient for Northeast in column 2?
  6. Interpret β2 in column 1.
  7. What additional information is needed to test if black workers and Hispanic workers earn different incomes in column 1? What regression could you run to simplify the test?
  8. This must be typed. Use the project data set to estimate the equation with all of the variables from columns 1,2,3. of the regression results table and one other regression that you may find of interest for your project. (Your data set is a subsample of this set.) ”grade” is the education variable, the census variable has the regional categories.

To create dummy variables for race type ”tab race, gen(rdum)”. This will create rdum1. rdum2, rdum3, rdum4, and rdum5, each will have the associated race in the variable label. Use the same technique for census group.

(a) Create a table similar to Table 1 with regression results. The table does not need to be identical, but all of the following must be met to receive credit:[1]

  • Include all of the listed variables.
  • Use variable labels that make sense to someone that has never used the data (ie Years of Education instead of ihigrdc).
  • Put standard errors in parentheses.
  • Denote coefficients that are statistically significant at 0.01 ***, 0.05 **, and 0.10 * significance levels.

Table 1: Regression Results For Homework 4

  (1) (2) (3) (4)
  Adult Income Adult Income Adult Income Adult Income
Education 3914.8 3934.4 2626.2 3885.8
  (226.7) (227.0) (275.9) (227.1)
Black -6886.0 -7583.6 -790.1 -7192.8
  (1597.8) (1668.6) (1716.4) (1635.8)
Hispanic -2270.6 -2144.4 2318.2 -2424.3
  (1727.4) (1809.5) (1764.7) (1731.5)
Mixed race (non-Hispanic) -1836.1 -1683.2 -2405.2 -1979.6
  (6978.8) (6982.2) (6842.2) (6979.6)
Female -15382.8 -15434.5 -14758.5 -15478.4
  (1291.0) (1291.2) (1266.8) (1294.4)
Age 1445.7 1472.3 1378.0 1478.4
  (461.1) (461.0) (452.4) (461.2)
Northeast   3267.4

(2184.2)

   
North central   -195.0

(1955.8)

   
South   2500.6

(1864.7)

   
Armed Services Aptitude Battery     0.149

(0.0291)

 
HH Income as Adolescent     0.112

(0.0164)

 
Vanilla       2217.6

(1692.8)

Strawberry       -791.6

(1742.8)

Butter pecan       1304.7

(2439.6)

None of these       3718.6

(2397.3)

Constant -57155.2 -59457.3 -52242.0 -58456.2
  (14572.0) (14636.8) (14289.6) (14606.5)
Observations 1995 1995 1995 1995
ESS 3.79899e+11 3.83837e+11 4.46293e+11 3.84050e+11
RSS 1.62137e+12 1.61743e+12 1.55497e+12 1.61721e+12
R2 0.190 0.192 0.223 0.192

Standard errors in parentheses

Table 2: Project Sample

  (1) (2)
  Earnings per hour Log(Earnings Per Hour)
Highest grade completed 113.5∗∗∗ 0.0574∗∗∗
  (1.044) (0.000538)
Age 80.32∗∗∗ 0.0545∗∗∗
  (1.044) (0.000538)
Age2 -0.765∗∗∗ -0.000529∗∗∗
  (0.0122) (0.00000628)
Female -276.2 -0.168∗∗∗
  (5.429) (0.00280)
[1em] Black -180.4 -0.0963∗∗∗
  (8.843) (0.00455)
American Indian -106.1∗∗∗ -0.0495∗∗∗
  (25.20) (0.0130)
Asian -11.76 -0.0206∗∗∗
  (13.22) (0.00681)
Other Race -34.41 -0.0182
  (18.27) (0.00941)
Adjusted R2 0.211 0.255

Standard errors in parentheses

p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01

 

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[1] All of these can be done with the esttab command. See the sample estout.do file and previous homework’s on carmen for help.

Case 5-1:Harrington Company- Buy your research paper oline [http://customwritings-us.com/orders.php]


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Case 5-1

  1. A. Harrington Company
  2. A. Harrington Company is a U.S.-based company that prepares its consolidated financial statements in accordance with U.S. GAAP. The company reported income in 2015 of $5,000,000 and stockholders’ equity at December 31, 2015, of $40,000,000.

The CFO of S. A. Harrington has learned that the U.S. Securities and Exchange Commission is considering requiring U.S. companies to use IFRS in preparing consolidated financial statements. The company wishes to determine the impact that a switch to IFRS would have on its financial statements and has engaged you to prepare a reconciliation of income and stockholders’ equity from U.S. GAAP to IFRS. You have identified the following five areas in which S. A. Harrington’s accounting principles based on U.S. GAAP differ from IFRS.

  1. Restructuring
  2. Pension plan
  3. Stock options
  4. Revenue recognition
  5. Bonds payable

The CFO provides the following information with respect to each of these accounting differences.

Restructuring Provision

The company publicly announced a restructuring plan in 2015 that created a valid expectation on the part of the employees to be terminated that the company will carry out the restructuring. The company estimated that the restructuring would cost $300,000. No legal obligation to restructure exists as of December 31, 2015.

Pension Plan

In 2013, the company amended its pension plan, creating a past service cost of $60,000. The past service cost was attributable to already vested employees who had an average remaining service life of 15 years. The company has no retired employees.

Stock Options

Stock options were granted to key officers on January 1, 2015. The grant date fair value per option was $10, and a total of 9,000 options were granted. The options vest in equal installments over three years: one-third vest in 2014, one-third in 2015, and one-third in 2016. The company uses a straight-line method to recognize compensation expense related to stock options.

Revenue Recognition

The company entered into a contract in 2015 to provide engineering services to a long-term customer over a 12-month period. The fixed price is $250,000, and the company estimates with a high degree of reliability that the project is 30 percent complete at the end of 2015.

231

Bonds Payable

On January 1, 2014, the company issued $10,000,000 of 5 percent bonds at par value that mature in five years on December 31, 2018. Costs incurred in issuing the bonds were $500,000. Interest is paid on the bonds annually.

Required

Prepare a reconciliation schedule to reconcile 2015 net income and December 31, 2015, stockholders’ equity from a U.S. GAAP basis to IFRS. Ignore income taxes. Prepare a note to explain each adjustment made in the reconciliation schedule.

 

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Engineering Assignment help


Engineering Assignment help

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Case Study: Comprehensive Plan of Care and Paper


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Comprehensive Plan of Care and Paper

You have been provided with case studies in Week 4 and Week 5 that focused on genitourinary, and musculoskeletal disorders. You will pick one of these cases to analyze and create a comprehensive plan of care for acute/chronic care, disease prevention, and health promotion for that patient and disorder. Your care plan should be based on current best practices and supported with citations from current literature, such as systematic reviews, published practice guidelines, standards of care from specialty organizations, and other research based resources. In addition, you will provide a detailed scientific rationale that justifies the inclusion of this evidence in your plan. Your paper should adhere to APA format for title page, introduction, headings, citations, conclusion, and references. The paper should be no more than 4 pages excluding title page and references.

Criteria:

  • SOAP note
  • Evaluation of priority diagnosis
  • Facilitators and barriers to disorder management

 

Please Follow Grading Criteria Maximum Points
Introduction

The submission included a general introduction to the priority diagnosis.

10
Subjective Data

The submission included the patient’s interpretation of current medical problem. It included chief complaint, history of present illness, current medications and reason prescribed, past medical history, family history, and review of systems.

15
Objective Data

The submission included the measurements and observations obtained by the nurse practitioner. It included head to toe physical examination as well as laboratory and diagnostic testing results.

15
Assessment

The submission included at least three priority diagnoses. Each diagnosis was supported by documentation in subjective and objective notes and free of essential omissions. All diagnoses were documented using acceptable terminologies and current ICD-10 codes.

20
Plan of Care

Plan included diagnostic and therapeutic (pharmacologic and non-pharmacologic) management as well as education and counseling provided. The plan was supported by evidence/guidelines, and the follow-up plans were noted.

25
Evaluation of Priority Diagnosis

The plan chose the priority diagnosis for the patient and differentiated the disorder from normal development. Discussed the physical and psychological demands the disorder places on the patient and family and key concepts to discuss with them. Identified key interdisciplinary team personnel needed and how this team will provide care to achieve optimal disorder management and outcomes.

25
Facilitators and Barriers

The submission interpreted facilitators and barriers to optimal disorder management and outcomes and strategies to overcome the identified barriers.

20
Conclusion

The submission included what should be taken away from this assignment.

10
APA/Style/Format

The submission was free of grammatical, spelling, or punctuation errors. Citations and references were written in correct APA Style.
Utilized proper format with coversheet, header.

10
Total 150

 

 

 

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CASE STUDY 1

Musculoskeletal Disorders

After diagnostic testing, your patient was diagnosed with low back pain without any specific injury. One of the most important aspects of the care at this point is to create a comprehensive teaching plan. What are the important teaching points you need to consider for the acute care of this individual? And what would you suggest for prevention of potential future injuries?

Buy your research paper Online [Order: http://customwritings-us.com/orders.php]CASE STUDY 2

Genitourinary

Discuss the various types of sexually transmitted diseases. Your response should include the most common pathogens, typical signs and symptoms, and treatment.

  • What are the potential sequels from these diseases?
  • How will you integrate knowledge from evidence-based practice in creating a holistic plan of care for patients with sexually transmitted diseases?

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Buy your research paper OnlineAssessment: Developing your Leadership Philosophy


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Assessment: Developing your Leadership Philosophy

Today, the term philosophy often refers to the study of the origins and nature of a particular body of knowledge. A leadership philosophy is a statement of how you see yourself with respect to the context of leadership. This philosophy will influence your behaviours and thoughts regarding leadership. Although our philosophies are influenced by both external and internal forces, leadership philosophies reflect peoples’ values, beliefs and experiences related to leadership. A leadership philosophy can (and most likely will) change for a person as he/she grows and gains experience in different contextual settings. We suggest you use the following as a guide to help you develop your leadership philosophy (Please note: much of this has been completed in class e.g. personal values, assumptions, and beliefs etc.):

 

Personal best leadership experience ( I was a boarding captain at… school then you can make up the rest)

  1. Briefly describe the context/situation of this experience (e.g., what was going on, who was there, when was it, how did things turn out).
  2. List the most important actions or behaviours (i.e. 5 – 6) that you took as a leader in this situation. In other words, what did you do that made a difference in this situation?
  3. What words would you use to describe this experience? List as many as you can think of that apply.
  4. How did this experience affect your understanding of leadership and/or your subsequent leadership behaviour?

Personal inspiration or inspirational leader

  1. Who was this person and what was the nature of the relationship between the two of you?
  2. What specific traits or behaviours do you recall as being most characteristic of this individual?
  3. What impact did this person have on you as a leader? What lesson did you learn?
  4. What did this person want or expect from you?
  5. How do you feel about this person now? What would you like to say to this person now as you think back on your experience with him or her?

Information for writer to write.

 

  1. My father (name) …. ( I will put my dad name myself)
  2. When he was a commissioner of Metropolitan police back in 2011, there was 2 groups of protester red and yellow shirt, he had to command more than 20,000 policemen. I saw him on TV not just commanding policemen but he was actually there with along side with all the policemen. This show me he have determination and high leadership because with his position he don’t have to be there he can sit and command, but he should to be there with them as well as whenever there is an issue he always put his name up first before him men, he will protect his men when there are people saying bad things to his men.
  3. From that incident it show me that to be a successful leader you need to be good to your men don’t treat your subordinator bad jus because you are higher position than them, just like when you building a house you need a solid foundation otherwise the house going to clasp.
  4. Be a good man do whatever you what to do as long as you are not breaking the law and not violate others people right.

5.He is my hero and I want to make him proud of me, I will followed his step just like my older brother did.

 

Personal values, assumptions, and beliefs

 

Personal values are qualities or characteristics that you value in yourself. Most people would rather leave an organization or step down as a leader than violate their most important personal values. Your values guide your intentions, perceptions and behaviours. Most importantly to this context, they influence how you lead and follow. When your personal values are clear and you are conscious of them, it provides a solid foundation for leading. Think about the Rokeach Value Survey (RVS) that you took and complete the following steps. What are your most important values and what do they mean to you? What role can each of those values play in enacting your understanding of leadership? You can expand the table below to include as many values as you wish.

 

 

 

Values

List your values here

Personal Values Definition

Define your values here

How do you see your values influencing your leadership?
1.       Fairness  

 

 
2.       Loyalty  

 

 
3.       Responsibility  

 

 
4.       Honesty  

 

 

 

 

 

Assumptions are ideas that are assumed or believed to be true. As a leader it is important to understand what assumptions affect your leadership thinking. Often leaders are not aware of the assumptions because they are operating from certain paradigms that will not allow them to see assumptions. Reflection into one’s leadership is an excellent way to uncover assumptions.

 

  1. First, reflect on your personal best leadership experience and your inspirational leader. You can also think about a personal worst experience and worst leader as well. Just like bosses, we can sometimes learn the most from the extreme experiences at either end of the continuum. For each of the questions in this section, ask yourself:

 

  1. What were my assumptions?

 

  1. What influenced my assumptions?

 

  1. Would others (co-workers, friends, supervisors) see the situations and people I described differently?

 

  1. Next, write down your definition of leadership.

 

 

  1. When you are finished, review and reflect on your definition and identify the assumptions that are implicit in it. They may not be readily apparent. It might also be helpful to have someone else read your definition and then ask them what assumptions they can identify.

 

 

 

 

 

 

 

 

 

Beliefs are ideas that we hold to be true; they shape our perception of reality. If a leader believes that the only individuals in an organization who can make decisions are the management staff members, then that belief will influence how the leader treats others. Beliefs can also be unconscious; they are our habitual ways of thinking and acting that may be inhibiting our effectiveness. Answer the following questions about your leadership beliefs. Reflecting upon these questions (not merely answering them) will help you clarify the beliefs you hold about leadership.

 

  1. Should leaders have certain qualities to be able to lead? What are they?

 

  1. Who decides who leads? Who decides who follows?

 

  1. Does leadership have been be done by a single person or can it be done by more than one person?

 

  1. What is it that leaders actually do?

 

  1. What role do followers play in leadership?

 

  1. What factors in the situation are most likely to affect leadership?

 

  1. How do leaders gain credibility?

 

  1. What do you think is the purpose for leadership?

 

  1. In general, is there something good about leadership?

 

  1. Can people who have caused others harm be leaders, e.g. Adolph Hitler?

 

  1. Is leadership behaviour developed through personal experiences or through external forces?

 

For each of the questions above, write down one statement that best illustrates your belief about that question. For example, if you answered #8 with: “The purpose of leadership is to provide vision, guidance, and bring people together for a common good. It unites people and gets them to join together for a goal”, then your belief statement might be stated as: “I believe that leadership provides a vision to create a common good”. Write a statement for each question. You will use these statements in combination with the other activities to create your philosophy of leadership.

 

Now that you’ve identified your leadership values, uncovered your leadership assumptions and understood what beliefs guide your leadership thinking, you are now ready to write statements reflecting your leadership philosophy. Your leadership philosophy should be a statement that consists of your responses from the above exercise. It does not have to include everything, but it should encompass the general idea of what you’ve written.  We suggest that you reflect on the above guidelines exercises to write a narrative or essay that gradually unfolds your leadership philosophy (please note, while the term narrative is used here your writing needs to be scholarly).

 

As you unfold your leadership philosophy you are required to make reference to the existing leadership literature to support you observations and arguments. You also need to identify which theory (or theories) of leadership your philosophy most aligns with (e.g. Charismatic leadership, situational leadership, autocratic leadership, participative leadership, distributed leadership etc. etc.) and why. You are also required to reflect upon the critique of the theory (or theories) of leadership (all theories are subject to critique) and then discuss how you intend to address this critique within your philosophy of leadership.

 

With the above in mind your leadership philosophy might adhere to the following structure:

 

  1. Introduction, this simply needs to be an introduction to your paper that outlines what you are about to discuss
  2. Reflecting on my personal best leadership experience
  3. Personal inspiration or inspirational leader/s
  4. My personal values, assumptions and beliefs about leadership
  5. My Philosophy most aligns with …….. because ……
  6. Critical insights that I need to consider
  7. Conclusion

 

Your paper should be no more than 2,000 words in length (not including your reference list or any appendices that you might wish to attach). This means you must write with clarity and stick to the key points that demonstrate your leadership philosophy and how you have identified and intend to address any potential critique.

 

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ULMS550 2016/17 Task 2 – Critical reflections on European HR practices


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 ULMS550 2016/17 Task 2 – Critical reflections on European HR practices

Julie Sinclair is the HR Director for TVS SCS  http://www.tvsscs.com

 

Activity 1:– Draw a mindmap of the UK employee relations expectations and practices

Activity 2:- Draw a mindmap of German employee relations expectations and practices

Activity 3 Develop a table of comparison to illustrate convergence and difference

(N.B. words in activities 1, 2 and 3 do not count in your 600 words)

Activity 4:- Write 600 words to be address to Julie Sinclair:- The question Julie would like addressing is “What challenges do the key Industrial Relations differences between Germany and the UK present?”.

 

Suggested guidance and enquiries

  1. Compare and contrast the differences between works Council versus Trade Union (Activity 1, 2 and 3)
  2. Consider the impact and importance of the Works Council versus Trade Union in Germany.
  3. Consider the HR practices that are used within a specific sector like the motoring industry.  Is there a right way?
  4. Do you consider that there is one global HR approach?
  5. Do and should HR practitioners be the holder of ethics in an industry that is consumer driven and financially managed?
  6. Are there other models and industries we can look to where there is much greater effort being made to address the employment relationship?

To help you contextualise this work Julie was asked the following questions:-

Q 1:- What situation has created the context of why the question is pertinent

A 1:-TVS SCS have recently taken on a contract with General Motors in Germany.  They are providing HR support to Transfer of Undertakings Protection of Employment (UK) (TUPE) over existing employees and then offering ongoing HR support.

 

Q 2:- What has lead you to ask this question regarding TUPE between UK and Germany employees all belonging to the same organisation?

A 2:- There are challenges in Germany dealing with the works council when it comes to employee relations issues in particular relating to terms and conditions. Any changes to terms and conditions, recruitment of new employees, introduction of new working practices have to be approved by the works council. They can have more influence than Trade Unions, in the UK it is the other way around.

 

Q 3:-What do you consider industrial relationships is in practice?

A 3:- Relationship with the works council and trade union and ongoing communication to the impacted workforce. It is important that we engage with all stakeholders and achieve a positive outcome.

 

Q 4:- What have been your experiences of the differences in employment relations between UK and Germany?

A 4:- Employment Law in Germany is very different to the UK and in addition we have the language barrier.

 

Q 5:- What expectations do you have from the question set out?

A 5:- I would expect to see an overview of the differences between working with TU/Works Council in Germany versus the UK and how this can impact on communication between management and the employees. Also the challenge of a UK firm taking over a German operation and the challenges an external HR consulting practice could face supporting General Motors through this transition period.

My question to you as students….Whilst Julie is with us what else do you need to ask to complete this task…

 

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Buy your research paper Online-Case Study


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Case Objectives:

The Cravia case is taught in a module on leading growth and transformation in businesses in entrepreneurship programs at Harvard Business School (HBS). It can be used to explore how an entrepreneur develops and iterates on a successful business model, and how he or she thinks strategically about growth.

The case could also be used in courses focused on entrepreneurship, emerging markets, franchising, and the restaurant industry. Restaurants make up a large proportion of small businesses, and franchises are an intriguing option to get into the restaurant business because they offer a structured, proven business model for an entrepreneur to build upon. In addition, the case provides background on operating businesses in emerging markets. From the mid-1990s through the 2010s, Dubai rapidly grew from a backwater petro-state on the shores of the Gulf to a global city that was politically stable and socially liberal enough to attract Western tourists and businesses. As more and more Westerners began to see the Middle East as an important market and potential place to live, Dubai emerged as a very attractive location for regional headquarters—much like Singapore did in Southeast Asia in the 1990s..

 

Refer to PDF file Case Study:

Cravia: Launching High Growth Ventures in the Middle East

 

The attached case document is authorized for educator review use only by Saher El Annan, HE OTHER until November 2014.Permissions@hbsp.harvard.edu or 617.783.7860

 

QUESTIONS:

Discuss and evaluate the approach used by Walid Hajj to found and scale Cravia, and explain how much of Cravia’s success was due to Hajj’s decision to locate in Dubai.

 

Question 2

Explain the challenges that will Hajj and the Cravia team face as they expand outside Dubai within the region, and discuss opportunities and threats Hajj faces in 2014.

 

Question 1: The discussion should be related to Looking at Cravia’s timeline which shows that the company has explored growth in multiple dimensions: geographic growth (i.e., entering new markets) and product growth in the same markets (i.e., new brands), while also exploring new products for new markets (e.g., ZwZ). These two dimensions of growth can be represented in a product/market growth positioning matrix (see TN Exhibit 1). As shown in TN Exhibit 1 produced by the instructor, Cravia has, at times, pursued all four (five if you count “exit”) types of growth. Its early growth was driven by opening more Cinnabons and SBCs in Dubai. This would fall in the “enhance” quadrant. “Enhancements to current products or channels represent incremental adjustments to an existing strategy. An entrepreneur often chooses this approach as a venture begins to gain traction in a market and transitions to growth. Moreover, strategic expansions are opportunities to launch a new product in the existing market or to launch the existing product in a new market. [. . .] By expanding into adjacent product categories or markets, the entrepreneur should be able to leverage existing

strategic positions and capabilities. Students should explore the difference between scaling an existing business and expanding the scope of a business. Students should be able to explain economies of scale versus economies of scope.

Question 2Students should state the importance of Cravia’s growth strategy, students should consider how leaders set direction, execute, and deliver results and how this changes based on what they can leverage and what they must build new. To set direction, leaders “1) [identify] long-term goals, midterm strategies, and short-term objectives, 2) [assemble] the resources and [build] the capabilities needed to execute strategy and achieve the goals and objectives, and 3) [identify] the metrics and milestones they [will] use to measure their progress.”5 Leaders then: Execute and deliver results. These results are compared with the metrics and milestones that were set before execution; the comparisons enable students to understand leader/manager and his or her team to develop insights that are used to refine the business model. These insights uncover two types of gaps: execution gaps occur when the strategic assumptions and direction are confirmed but there has been a flaw in execution; strategy gaps occur when the strategic assumptions are flawed. On the basis of what they are learning, entrepreneurs pivot—either refining the strategy or refining the capabilities and resources needed to execute the strategy

 

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Homework help_ LINEAR PROGRAMMING: Click the link_ http://customwritings-us.com/orders.php


Module 4 – Home

LINEAR PROGRAMMING

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Modular Learning Outcomes

Upon successful completion of this module, the student will be able to satisfy the following outcomes:

  • Case
    • Write the profit and loss factors pertaining to a production decision in algebraic form.
    • Given the relevant profit and loss factors, write the profit function for a production decision.
    • Write the constraints pertaining to a production decision, using algebraic inequalities.
    • Given the profit function and constraints of a production decision, use an online application to solve the optimization problem.
  • SLP
    • Conclude a Delphi decision-making process.
    • Summarize and present the results of a Delphi decision-making process.
  • Discussion
    • Review of the course.
    • Discuss the limitations of linear programming when applied to actual allocation problems.

Module Overview 

Life is about constraints. We could make up millions of examples. When a couple earning a total of $5,000 per month sit down to do the household budget, they’re faced by one immediate constraint; the sum of all their monthly expenditures must be less than or equal to $5,000. A roofer is constrained by the size of his crew, the number of hours they’ll work per day, and the weather forecast. Students are constrained by the number of hours available for study, the courses they’re taking, and their academic schedules; that is, which assignments are due, and when.

Most of the time, we don’t handle constraints rationally. We don’t usually sit down and make plans for maximizing our productivity (or profitability, or whatever) while staying within our constraints. That’s what this module is about; how to make those plans.

To get a taste of the problem, let’s consider an example (Staple, 2014a).

A calculator company produces a scientific calculator and a graphing calculator. The market demands at least 100 scientific and 80 graphing calculators per day. Because of various limitations, no more than 200 scientific and 170 graphing calculators can be produced per day. To satisfy a contract with UPS, at least 200 calculators must be shipped each day.

Each scientific calculator sells at a $2 loss, but the company makes them anyway, to maintain market position. Each graphing calculator sells at a $5 profit. How many of each type should be made daily, to maximize profits?

How on Earth do you even begin to solve a problem like that? The short answer is, you don’t. A computer solves it. The application uses a procedure called linear programming. But how, you may ask, does linear programming work? The answer: It works just great!

NOTE: SECTIONS IN ITALICS ARE BACKGROUND. YOU CAN SKIP THEM AT FIRST READING (BUT SHOULD STUDY THEM LATER).

(Digression about Apps)

Even today, most textbooks teach various ways to solve linear programming problems using pencil and paper. That’s fine, from a pedagogical point of view, but let’s be honest – if faced with a real problem, involving real money, with real jobs on the line, would you attempt to find a solution using pencil and paper? Of course not. You’d either use a computer, or tell HR to hire a consultant, who would then use a computer.

(End of digression.)

Not all problems have solutions, including linear programming problems, and the computer will definitely tell you if the problem you’re trying to solve doesn’t have one. If it doesn’t, then there are two possibilities: either the problem itself is bogus, or you made a mistake when you entered the problem into the computer. The problems in this module aren’t bogus – they have solutions. And we’re going to spend a lot of time explaining and practicing the proper way of entering problems.

What’s Going On.

It’s worthwhile to stop and explain, in rough qualitative terms, exactly what linear programming does. This is background. No need to panic, since you won’t have to do anything like this in the assignments. In fact, you may want to skip ahead to the next session, entitled Setting Up Constraints. I strongly recommend, however, that you return to this section later. Sooner or later, you’ll need to know what’s going on “inside the box.”

Let’s take a closer look at the example. Begin with the constraints. I’ve numbered them in the “story” below, and then listed them separately.

A calculator company produces a scientific calculator and a graphing calculator. The market demands at least 100 scientific (1) and 80 graphing (2) calculators per day. Because of various limitations, no more than 200 scientific (3) and 170 graphing (4) calculators can be produced per day. To satisfy a contract with UPS, at least 200 calculators (5) must be shipped each day.

Just to make things simpler, let’s define two abbreviations: “SCI” = number of scientific calculators manufactured and shipped per day, “GPH” = number of graphing calculators manufactured and shipped per day. (We can use any abbreviations we like. These just happen to be easy to remember.) Here are the constraints.

  1. SCI must be at least 100.
  2. GPH must be at least 80.
  3. SCI cannot exceed 200.
  4. GPH cannot exceed 170.
  5. SCI plus GPH must be at least 200.
You may remember (if not, it’s OK) that relationships between two numbers can be shown as a plot on an X-Y plane. Here, we’re using SCI and GPH instead of X and Y. Every point on the plot represents one value of SCI and one value of GPH. For example, the black dot represents 50 scientific and 75 graphing calculators. (To review these ideas, see Staple, 2014b.)

The heavy vertical line shows the equality SCI = 100. The shaded area to the right, which includes the heavy line, consists of all combinations of SCI and GPH for which SCI is at least 100; or to put it another way, greater than or equal to 100. This is abbreviated

SCI >= 100.

Notice that the shaded area is bounded on the bottom by the horizontal axis, which represents GPH=0. This ought to make perfect sense, because you can’t make a negative quantity of anything. The minimum number of calculators of any type that you can manufacture is zero.

Here are the areas of the plot that correspond to the other constraints.

Each of the plots above represents a separate constraint. When we’re planning calculator production, however, we can’t consider the constraints one at a time; we have to consider all of them at once.

To visualize them all at once, we plot them together, as shown on the right. The numbers indicate the constraints, and the arrows show where the permitted points are located with respect to each equality line. If this isn’t clear, please compare (1) ð with the first plot above.

The region where all the permitted points overlap is called the Feasibility Region. For future use, we’ve labeled the corners of the feasibility region with letters; A, B, C, D and E.

 

The points in the feasibility region, which include the points on the boundary lines, represent all the possible combinations of scientific and graphing calculators that the company could possibly manufacture, given these constraints. Examples: The green dot, representing 150 scientific calculators and 100 graphing calculators, is a permitted combination; the red dot, representing 50 calculators of each type, is not.

We still haven’t found the optimum combination of calculators, and we’ll return to that problem in a moment. But first let’s take a detour, and consider a combination of constraints that looks like a linear programming problem, but isn’t. It is, to use an earlier, non-technical term, a “bogus problem.”

It’s not hard to construct a bogus problem. We’ll simply take the problem we’ve been looking at, and remove one of the constraints. Let’s remove constraint (4), which specifies that the number of graphing calculators cannot exceed 170.

 

With that constraint removed, we no longer have a problem that can be solved using linear programming. That’s because there are an infinite number of points in the feasibility region. The boundaries on the left and right are the SCI constraints: between 100 and 200, inclusive. There are bottom boundaries to the region, but no top boundary. The company could, in theory, make an infinite number of graphical calculators! This is bogus. And the computer app would tell us it’s bogus.

 

 

 

Having looked at something that isn’t a liner programming problem, let’s return to the solution of one that is.  

On the right, we’ve expanded the labels on the corners of the feasibility region to include their coordinates; these are the number of scientific and graphics calculators associated with each. For point A, that would be 100 scientific and 170 graphics calculators. Let’s list them in a table.

         

         Number of Calculators

 

Point    Scientific   Graphic             

  A         100        170                    

  B         200        170                         

  C         200         80                           

  D         80         120                        

  E         100        100  

 

The coordinates can be determined by inspection (that is, simply looking), or from the equations of the constraints, by using various algebraic techniques that we won’t discuss here.

The points A, B, C, D, and E are called the extrema (sing. extremum). It’s a useful fact that the optimum mix of scientific and graphics calculators is associated with one of the extrema; that is, one of the coordinate pairs listed above will give the company their maximum profit, given these constraints.

To determine which coordinate pair that would be, let’s go all the way back to “the story problem.”

Each scientific calculator sells at a $2 loss, but the company makes them anyway, to maintain market position. Each graphing calculator sells at a $5 profit.

From this information, we can write the so-called profit equation. Let p = profit, SCI = the number of scientific calculators, GPH = the number of graphing calculators by GPH. Then the equation is,

p = -2(SCI) + 5(GPH)

Example: Imagine a really terrible day, during which the company sells exactly one calculator of each type. They make $5 on the graphing calculator and lose $2 on the scientific calculator, for a total profit of $3. We can do that much in our heads. But let’s use the equation.

p = -2(SCI) + 5(GPH)

Since SCI = 1 and GPH = 1,

p= (-2)(1) + (5)(1) = -2 + 5 = 3.

(This is always a good way to make sure we’re using a correct equation. Try it out, using very simple variables. If it works as expected, then it’s probably OK.)

We now calculate the profit for each of the extrema.

Point SCI GPH p = -2(SCI) + 5(GPH)
A 100 170 (-2)(100) + (5)(170) = -200 + 850 = 650
B 200 170 (-2)(200) + (5)(170) = -400 + 850 = 450
C 200 80 (-2)(200) + (5)(80) = -400 + 400 = 0
D 80 120 (-2)(80) + (5)(120) = -160 + 600 = 440
E 100 100 (-2)(100) + (5)(100) = -200 + 500 = 300

Point A yields the greatest profit, $650. The optimum mix of scientific calculators and graphing calculators that the company should product, per day, is 100 and 170 respectively.

To summarize, this is how linear programming works:

  1. Specify the constraints in the form of valid equations.
  2. Define a feasibility region.
  3. Find the extrema; which are, the corners of the feasibility region.
  4. Test the coordinates of each extremum against the profit equation.
  5. The coordinates of the extremum that yields the maximum profit are the solution of the problem.

We’ve worked through all five steps. The good news is, the only important step is the first step. If we can do that, then a computer can do the rest.

(Digression.)

One final, non-mandatory bit of information, and we’ll move on. The procedure works with any number of variables, corresponding to any number of dimensions. The example we’ve been beating to death has two variables, SCI and GPH. The feasibility region is an area on a two-dimensional plane. If we had three variables, the feasibility region would be a volume in a three-dimensional space.

For example: Suppose that instead of manufacturing only two types of calculators, the company made three; scientific, graphing, and accounting. Further suppose there was a set of constraints, similar to those above, but involving three variables: SCI, GPH, and ACC.

The feasibility region, if one existed, would be the points on and inside a three-dimensional object. For reasons relating to the linear nature of linear programming, which we didn’t go into, the object would be a prism, bounded by flat surfaces. The corners where the surfaces came together would be the extrema, and the optimum solution of the profit equation would consist of the coordinates of one of those extrema.

It’s not uncommon to encounter a linear programming problem with even more variables; for example, we could imagine having to optimize the production of eight different types of calculators. In that case, the feasibility region would be a prism in eight-dimensional space. Such a region is, of course, impossible to draw, or even to imagine; but the algorithm doesn’t care. If a solution exists, the computer will find it.

(End of digression.)

If you’re feeling a bit panicky by now, take a deep breath and get over it. Everything you’ve just read in this section is background. The only thing you’ll need to know is what follows: that is, how to set up a linear programming problem in a form the computer can understand. We’re moving on to that right now.

Setting Up Constraints

If there’s one thing sixth graders detest, it’s “word problems,” or “story problems.” Adding, subtracting, multiplying and dividing numbers is one thing. Reading about a real-world situation, and then deciding which numbers are involved and what to do with them, is something else entirely. The sixth graders get no sympathy from their teachers. The teachers know that business, science, engineering and everyday life never hand us pages of numbers to crunch. They hand us situations. We have to think though the situations, decide which numbers are relevant, and perform the necessary calculations.

Let’s take it from the top. Here, once again, is the example we’ve been working to death:

A calculator company produces a scientific calculator and a graphing calculator. The market demands at least 100 scientific and 80 graphing calculators per day. Because of various limitations, no more than 200 scientific and 170 graphing calculators can be produced per day. To satisfy a contract with UPS, at least 200 calculators must be shipped each day.

Each scientific calculator sells at a $2 loss, but the company makes them anyway, to maintain market position. Each graphing calculator sells at a $5 profit. How many of each type should be made daily, to maximize profits?

The first step is to identify the variables; these are the things for which we need to find numbers. Don’t be confused by the fact that there are lots of numbers in the problem, such as the minimum number of each type needed daily; these aren’t variables, they’re constants. They’re given; we don’t need to find them. The numbers we need to find are the following.

  • Scientific calculators produced, per day
  • Graphing calculators produced, per day
  • Daily profit (to be maximized)

Because we’re going to be writing equations, the next step is to come up with good labels, or abbreviations, for the variables. Theory doesn’t tell us what sort of labels to use, and almost any label would work. Some computer programs even permit variable labels with several words; the only requirement is they be enclosed with quotation remarks; as an example, “Scientific calculators produced, per day.” We won’t go that route, for two reasons. First: it takes a lot of space to type out such long labels, and it produces some confusing clutter. Second: a simple error, such as misspelling one of the labels or forgetting to close a set of quotation marks, would cause an error that could be difficult to find. So we’ll use labels that are both easy to remember, and short.

Returning to the example: because it’s the same for all the variables, we can take the time dimension “daily” or “per day,” as a given, and drop it.  We can also take “produced” as a given; it’s a calculator company, so it’s producing calculators, and it’s also trying to “produce” a profit. Because calculators are all we’re interested in at the moment, we can also drop the word “calculators” as being redundant. So the variables boil down to

  • scientific
  • graphing
  • profit (maximized)

Some programs don’t permit any flexibility with respect the variable that’s being either maximized or minimized. It has to be represented by one letter. In this case, we’ll let “Profit” be simply “p,” and the final list becomes

  • scientific
  • graphing
  • p

In many textbooks and online presentations (Staple, 2014b), the authors refer the variables to the traditional Cartesian coordinate axes; for example, “scientific” = x, “graphing” = y. I see no point in doing that. If you accidentally swap X and Y when writing your equations, then the program won’t work; or even worse, it may work, but produce incorrect results.

Let’s stop and summarize. The first steps of solving a linear programming problem are:

  1. Read the narrative carefully.
  2. Identify the variables.
  3. Define simple labels that unambiguously define the variables.

Let’s make steps 2 and 3 more systematic by putting the full variables and corresponding labels into a table. This is overkill for such a simple problem, but it may be useful for more complicated ones; further, it forces you to concentrate on the narrative, and be sure you’re not overlooking anything.

VARIABLE LABEL
Scientific calculators produced, per day scientific
Graphing calculators produced, per day graphic
Daily profit (to be maximized) p

Once we’ve defined the variables, there’s a lot more to do. We still have to write the equations that represent the constraints, and enter them into a computer program. But before we go on to do that, let’s practice defining variable labels.

Example 2 (After Staple, 2014b)

You need to buy some filing cabinets. The model made by Sauder costs $100 per unit, needs 6 square feet of floor space, and holds 8 cubic feet of files. The unit by Steelcase costs $200 per unit, needs 8 square feet of space, and holds 12 cubic feet. You have been given $1400 for the purchase, but don’t have to spend all of it. Your office has enough floor space for 72 square feet of cabinets. How many of each model should you buy, to maximize the storage volume?

VARIABLE LABEL
Number of Sauder cabinets required sauder
Number of Steelcase cabinets required steelcase
Storage volume (to be maximized) v

Example 3 (after Staple, 2014b)

At a certain refinery, the refining process requires the production of at least two gallons of gasoline for each gallon of fuel oil. With winter coming, at least three million gallons of fuel oil will be required per day. On the other hand, winter sees a decrease in the requirement for gasoline; no more than 6.4 million will be required, per day. If gasoline sells for $3.90 per gallon and fuel oil sells for $2.50 per gallon, how many gallons of each should be produced, per day, to maximize revenue?

VARIABLE LABEL
Millions of gallons of gasoline produced, per day gas
Millions of gallons of fuel oil produced, per day oil
Revenue per day, dollars (to be maximized) r

Example 4 (after Staple, 2015)

A lab rabbit need a daily diet containing at least 24 grams (g) of fat, 36 g of carbs, and 4 g of protein. It should not be fed more than 5 ounces (oz) of food daily.  The lab tech decides to blend two commercially available feeds, Bunny Chow and Hop-To-It. An oz of Bunny Chow contains 8 g of fat, 12 g of carbs, and 2 g of protein, and costs $0.20. An oz of Hop-To-It contains 12 g of fat, 12 g of carbs, and 1 g of protein, and it costs $0.30. What is the optimum blend of the two feeds; that is, the blend that meets a rabbit’s requirements, at minimum cost?

VARIABLE LABEL
Oz of Bunny Chow in the blend, per rabbit per day bunny
Oz of Hop-To-It in the blend, per rabbit per day hop
Feed cost per rabbit per day (to be minimized) c

Once we have variables, the next task is to express their relationships in a form a computer can understand.

Writing Equations for Inequalities

The “=” sign, meaning “is equal to,” is something we learn how to use in the second grade (or thereabouts). The entities on either side of the “=” sign can be numbers, in which case we have an identity. Probably the most familiar identity, again familiar from early childhood, is 2+2=4.

Another use of the “=” sign is in equations, where one or more unknowns are indicated by letters. Here are some examples.

  • X = 2+2 (Solution: X=4)
  • F = (9/5)C + 32 (Temperature conversion: F = degrees Fahrenheit, C = degrees Celsius)
  • R = P(1+T) (R = retail price, P = list price, T = sales tax)
  • USD = R(EUR) (Currency conversion: USD = US dollars, R = exchange rate, EUR = Eurodollars)

We’re interested in a particular type of equation called the constraint, in which a variable is specified to be either one number, or within a range of numbers. Here are some examples.

  • JAN = 31 (in which “JAN” is defined as, “The number of days in January.”)
  • CTS = 100 (“CTS” = “The number of cents in a dollar.”)

These specify the value of a variable as one number. To specify a range of numbers, we need signs other than “=.” Here they are, along with their meanings. (For a complete treatment of this topic, please see Khan,2015.)

  • < “Is less than”
  • <= “Is less than or equal to”
  • > “Is greater than”
  • >= “Is greater than or equal to”

Here are some trivial numerical examples.

  • 2 < 3
  • 3 <= 3 (It’s not less than, but it’s definitely equal!)
  • 4 > 3
  • 4 >= 3 (It’s not equal, but it’s definitely greater than!)

Here are some less trivial examples.

  • Vote >= 18 (where “Vote” = legal voting age)
  • Drink >= 21 (where “Drink” = legal drinking age)
  • Feb <= 29 (where “Feb” = number of days in the month of February)
  • Prez <= 8 (where “Prez” = number of whole years a president has been in office)

Now let’s combine all of the above, and write out constraints that can be used in a linear programming application. It’s a four-step process;

  • Identify the variables
  • Create variable labels
  • Translate the constraints into “less/equal/greater” language
  • Write the constraints in algebraic form.

Here are some examples.

  1. Joe’s Sports Bar is hiring a Chief of Security (aka bouncer). Joe will only interview karate black belts* 21 or older, at least 6 feet four inches tall, and weighing at least 220 pounds.
Variables Labels  “Less/equal/greater” Algebraic form
Age in years Age Age 21 or older (greater than or equal to 21) Age >=21
Height in feet and inches Height Height at least 6’ 4” (greater than or equal to 76”) Height >= 76
Weight in pounds Weight Weight at least 220 (greater than or equal to 220) Weight >= 220

*Note: Karate qualification isn’t a variable, because it doesn’t vary. No black belt, no interview!

  1. Joe’s Sports Bar is hiring table servers. Only the following candidates will be interviewed: women* between the ages of 21 and 35 years of age inclusive, not more than 5 feet 8 inches tall, weighing not more than 140 pounds. (Joe may be in trouble with the law concerning age and sex discrimination, but that’s a problem for another course.)
Variables Labels  “Less/equal/greater” Algebraic form
Age in years Age Age 21 or older (greater than or equal to 21)

Age 35 or younger (less than or equal to 35)

Age >=21

Age <=35

Height in feet and inches Height Height less than or equal to 68 (inches) Height <= 68
Weight in pounds Weight Weight less than or equal to 140 Weight <= 140

*Note: Sex isn’t a variable, because men won’t be interviewed.

  1. Peggy Potter makes coffee cups and vases. She’s able to make a maximum of 100 pieces per day.
Variables Labels  “Less/equal/greater” Algebraic form
Number of cups per day Cups (no constraint)  
Vases per day Vases (no constraint)  
    Cups plus vases is not more than 100 (less than or equal to 100) Cups + Vases <= 100
  1. Peggy Potter makes coffee cups and vases. She gets a special rate from UPS if she ships at least 50 pieces per day, so she had adopted that as a business constraint.
Variables Labels  “Less/equal/greater” Algebraic form
Number of cups per day Cups (no constraint)  
Vases per day Vases (no constraint)  
    Cups plus vases is at least 50 (greater than or equal to 50) Cups + Vases >= 50
  1. Peggy Potter makes coffee cups and vases. Because of the clay needed for each item, and the expected demand for each, Peggy decides she should make, at most, two cups for each vase.
Variables Labels  “Less/equal/greater” Algebraic form
Number of cups per day Cups (no constraint)  
Vases per day Vases (no constraint)  
    Number of cups not more than twice the number of vases (cups less than or equal to two times vases) Cups <= 2(vases)
  1. Eye Full Optics makes binoculars and telescopes. Both instruments ship with the same eyepieces; each telescope needs one eyepiece, each pair of binoculars needs two. EFO’s supplier can send them no more than 300 eyepieces per day.
Variables Labels  “Less/equal/greater” Algebraic form
Number of binoculars per day binocs Each pair requires two eyepieces (300 eyepieces max)  
Number of scopes per day scopes Each pair requires one eyepiece (300 eyepieces max)  
    Number of eyepieces required for both binocs and scopes is not more than 300 (less than or equal to 300) Scopes + 2(binocs) <= 300
  1. A calculator company produces a scientific calculator and a graphing calculator. The market demands at least 100 scientific and 80 graphing calculators per day. Because of supply limitations, no more than 200 scientific and 170 graphing calculators can be produced per day. A shipping contract requires at least 200 calculators be shipped per day.
Variables Labels  “Less/equal/greater” Algebraic form
Number of scientific calculators produced per day SCI

(Reminder: A label can be almost anything)

At least 100 (greater than or equal to 100)

No more than 200 (less than or equal to 200)

SCI >= 100

SCI <= 200

Number of graphing calculators produced per day GPH At least 80 (greater than or equal to 80)

No more than 170 (less than or equal to 170)

GPH >= 80

GPH <= 170

    Total calculators produced (SCI plus GPH) is at least 200 (greater than or equal to 200) SCI + GPH >= 200

The Profit Function

There’s one last thing we need to discuss; the profit function. The ultimate goal of linear programming is to maximize profit, by finding the particular values of the variables that give us the largest value of profit. (The actual entity may be something other than profit, and the goal may be to minimize rather than maximize. For example, we may be interesting in minimizing workspace, maximizing production volume, or minimizing waste. The same principles apply.)

Profit is a function of the variables, given the constraints. Suppose Peggy Potter earns $5 for every coffee cup she makes. Then her profit (p) for the day, in dollars, is simply the number of cups she makes, multiplied by 5, which in algebraic form is p = 5(cups). But what’s the constraint? Well, in this case, there isn’t one. Peggy could, in theory, make a million cups in a day, and earn $5M. But that’s not realistic. A realistic constraint would be, not more than 50 cups per day. Then Peggy’s profit is p = 5(cups), subject to cups <=50. If she puts in a long day at the wheel and makes 50 cups, she makes $250. If she takes the day off and doesn’t make anything at all, then she earns nothing.

Suppose Peggy makes both cups and vases, earning $5 for each cup and $7 for each vase. Then her profit function would be

P = 5(cups) + 7(vases)

…where “p” is the profit for the day’s work, and the variables “cups” and “vases” simply refer to the number of each, produced that day.

Going back to the calculator company: If the company loses $2 on each scientific calculator and earns $5 on each graphing calculator, then their daily profit is

p = -2(scientific) + 5(graphing)

…where, as before “p” is the profit for the day’s work, and the variables “scientific” and “graphing” refer to the number of scientific and graphing calculators produced each day. (If $5 doesn’t seem like much, remember that’s the profit; which is,the selling price minus the costs of production, shipping, advertising, and other expenses.)

Putting It All Together

We’ve come a long way. We’ve learned how to analyze a situation, define variables, set up constraints, and write the profit function. What we’ve skipped over (or rather relegated to an optional section) is the math that’s required to make use of all that information. We’ve skipped over it because a computer app is going to do it for us.

There are lots of linear programming apps on the Web. We’ll use Stefan Waner’s (2010).

(Digression.)

The example shown above illustrates something important. An app, such as Waner’s, allows us to evaluate a profit function at the extrema of a feasibility region that cannot be sketched, or even visualized. Let’s expand on that.

Up until now, we’ve been limited to two variables, x and y (cups and vases, etc.) The example above has four variables, labeled x, y, z and w. Just as x and y are perpendicular in two-dimensional space (the X-Y plane), the variables x, y, z and w are mutually perpendicular in four-dimensional space. The feasibility region is a volume in that four-dimensional space, with three-dimensional faces and corners defined by the intersections of those faces. Obviously, we can’t visualize them — but mathematical objects like that exist anyway, even if we can’t “see” them in the usual sense. And computer apps have no trouble working with them. You’ll find some three- and higher-dimensional problems in the Case exercises. You’ll solve them using an app.

(End of digression.)

Now, let’s finally do the entire scientific vs. graphing calculator problem.

A calculator company produces a scientific calculator and a graphing calculator. The market demands at least 100 scientific and 80 graphing calculators per day. Because of various limitations, no more than 200 scientific and 170 graphing calculators can be produced per day. To satisfy a contract with UPS, at least 200 calculators must be shipped each day.

Each scientific calculator sells at a $2 loss, but the company makes them anyway, to maintain market position. Each graphing calculator sells at a $5 profit. How many of each type should be made daily, to maximize profits?

As we’ve seen, the constraints are

  • “at least 100 scientific and 80 graphing calculators per day”
    • scientific >=100
    • graphing >= 80
  • “no more than 200 scientific and 170 graphing calculators produced per day”
    • scientific <=200
    • graphing >= 170
  • “at least 200 calculators must be shipped each day”
    • Scientific + graphing >= 200

The profit function is

  • “scientific calculator sells at a $2 loss, ….graphing calculator sells at a $5 profit”
    • p = -2(scientific) + 5(graphing)

The profit function goes on the top line. The format is prescribed; the line must read, “Maximize (the profit function) subject to.” The constraints go next, with each constraint on its own line.

Let’s check and make sure those values of the variables do, in fact, give that optimal solution.

p = -2(scientific) + 5(graphing)

= -2(100) + 5(170)

= -200 + 850

= 650.

We’re not expecting the computer to make a mistake, but it’s nice to check, if only to remind ourselves what the solution means.

So ends our discussion of linear programming. Be sure you understand it before moving on the problems; if you don’t, then you’re setting yourself up for major frustration. In addition, be sure you understand the information here, in this Module, before surfing the Web and looking for more. There’s a lot out there, but a lot of it confusing. (Why confusing? Because it includes lots of technical details that we don’t think are particularly important. You don’t need a degree in mechanical engineering to drive a car, and you don’t need a degree in math to do linear programming.)

What’s the takeaway? That is, what do we want you to remember, ten years from now? Well, we want you to remember that there’s a procedure called linear programming, and it’s highly effective for solving certain types of problems. When you encounter a problem of that type, then you’ll either go online and brush up on linear programming, or (more likely) tell HR to go out and hire a stats consultant. Either way, you’ll be a step ahead of your technically illiterate competition.

Module 4 – SLP

LINEAR PROGRAMMING

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Complete the wrapup of a three-round Delphi decision-making exercise, following the detailed example cited in the Home Page discussion(SEE UPLOADED WORD FILE).  As before, you may copy and / or adapt verbiage from the example without citing it.

SLP Assignment Expectations

The SLP writeup should consist of:

  • The Letters to the Participants, which include
    • Thanks for their participation
    • A summary of their third-round responses
    • A short narrative discussing the evolution of the decision-making process, how opinions shifted, what relevant factors the group identified, and what consensus (if any) the group arrived at.
  • Follow the instructions in the BSBA Writing Style Guide (July 2014 edition), available online at
    https://mytlc.trident.edu/files/Writing-Guide_Trident_2014.pdf.
  • There are no guidelines concerning length.  Write what you need to write – neither more, nor less.
  • In the SLP ONLY, references and citations are NOT required.  However:  If you state a fact, express an opinion, or use a turn of phrase that isn’t your own, then you should credit the source, just like you would in everyday conversation.  (Example:  “In the words of Monty Python, ‘And now for something completely different.’ “)

——-

TEST YOUR UNDERSTANDING: Answer

The linear equations corresponding to the constraints are:

  1. 2y = 3x
  2. 2x + 3y = 15
  3. 3y = x

Here’s the plot, with the lines, extrema, and the region labeled.  It was created with Relplot, and the labels were added using the Snagit graphics editor.  Using Relplot, it’s possible to create the sketch without knowing the coordinates of the extrema.  That’s because the app takes the line equations as input.

Here’s another version.  It’s less elaborate, but still perfectly acceptable.  If you want to upload a hand sketch, however, you’ll have to do the calculations first, so you’ll know where to put the extrema.

Here’s how to find the coordinates of the extrema:

A:  The only values of x and y that satisfy the equation 1 (that is, 2y=3x) is (0,0) .  Ditto for equation 3.  So the coordinates for A are

A(0,0)

B: This point is the simultaneous solution of equations 1 and 2;  that is, of

2y=3x

2x + 3y = 15.

We’ll use the Webmath solver (Discovery, 2014) to find the values of x and y that satisfy both equations.  There are many such apps on the Web;  look for them using Google, or your favorite search engine.

Here’s what the setup looks like:

Proceed in the same way to find the coordinates of point C, which is simultaneous solution of equations 2 and 3;  that is,

2x + 3y = 15

3y=x

The answer is C(5, 1.67).

Summary answer:  Extrema are

A(0,0)

B(2,31, 3.46)

C(5, 1.67)

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