Acidity The Natural Way - 1066 Words

Acidity The Natural Way Stomach acids are essential for the digestion of food. Increased secretion of acids in the stomach gives rise to acidity. Acidity is manifested by several uncomfortable symptoms such as burning and pain in the chest and stomach; nausea; bitter taste in mouth; vomiting and discomfort in the stomach. Acidity, been one of the commonest digestive complaints. At some point in our lives, we have all suffered from these symptoms. Acidity is generally stimulated by consumption of spicy foods, junk food, carbonated drinks, fried foods, chocolates, stress or lack of sleep. Obesity, pregnancy and other medical conditions may also give rise to acidity. Irrespective of the reason, acidity can prove to be an uncomfortable experience. There are several natural remedies that work wonders in keeping acidity at bay and also in providing relief from acidity. Though, chronic acidity complaints may require proper medications. Some of natural remedies are as follows:- Bananas They prove to be an effective antidote for acidity, as it has a high pH value. More the pH value, lesser are the symptoms of acidity. Banana further, enhances the production of mucous by the stomach lining which reduces the harmful effects of acidity. The high fibre content of banana decreases the recurrence of acidity. Apart from banana, watermelon and cucumbers too are effective against acidity. Consumption of overripe bananas during an attack of acidity is even more beneficial. ColdShow MoreRelatedAcids And Its Effect On The Wine Industry1079 Words   |  5 PagesVolatile acidity of 0.03-0.06% is produced during fermentation and is considered a normal level. Tartaric and malic acids are produced by grapes as they develop. In warm climates, these acids are lost through the biochemical process of respiration. Grapes grown in warmer climates have lower acidity than grapes grown in cooler environments For example, Chablis (France) produces grapes with high acid because the climate is very cool, while Napa Valley produces grapes with lower acidity because theRead MoreThe Cause and Effects of Acid Mine Drainage1699 Words   |  7 Pagesancient times, but it was not until the 1800s when fast growing industrialization and heavy mining that it caught a lot of attention. Acid rock drainage is the term used to describe leachate, seepage, or drainage that has been affected by the natural oxidation of sulfur minerals contained in rock which is exposed to air and water. The major components of ARD formation are reactive sulfide minerals, oxygen, and water. Biological activity and reactions is what is responsible for the productionRead More The Cause And Effects Of Acid Mine Drainage Essay1712 Words   |  7 Pagesnot until the 1800s when fast growing industrialization and heavy mining that it caught alot of attention. nbsp;nbsp;nbsp;nbsp;nbsp;Acid rock drainage is the term used to describe leachate, seepage, or drainage that has been affected by the natural oxidation of sulfur minerals contained in rock which is exposed to air and water. The major components of ARD formation are reactive sulfide minerals, oxygen, and water. Biological activity and reactions is what is responsible for the production ofRead MoreThe Problem of Acid Rain716 Words   |  3 Pagesnitric acids present, the higher the acidity of the rain. On a 14 point scale, 7 being neutral, anything less than 7 is considered acidic and anything more is considered alkaline. Battery acid is about 1 acidity and lemon juice is around 2 acidity. Regular rain is between 5 and 6 acidity. Acid rain is somewhere between 2 and 5.5. The worst case of acid rain ever recorded was in Wheeling, West Virginia where the rain had an acidity of 2.2. These levels of acidity seriously harm plants, trees, and allRead MoreUnc Wilmington s Location Is The Presence Of Pollution1066 Words   |  5 Pagesand rising sea levels. This causes many global and local repercussions that transcend into other ecosystems around the world. As the ocean consists of two-thirds of our world, we need to work to save it now, before it affects us in an even greater way. One of the issues that is currently harming the ocean is the presence of pollution. Studies have shown that over the past thirty years, people have increased their use of plastics and synthetic materials and recently it has become even more abundantRead MoreThe Fourth Extinction : An Unnatural History By Elizabeth Kolbert1112 Words   |  5 PagesThe book identifies the effects of human activity on how, over humans history on earth, the natural world has been affected. Every environmental impact stems into three basic groups of global problems to nature: Pollution, Habitat loss and Invasive Species. Kolbert explains that each impact can be traced back to one source, human industrial development. With each impact various types of life in the natural world are affected. Deforestation, urbanization, and sea level rise contribute to habitatRead MoreOcean Acidification : Climate Change s Equally Evil Twin1198 Words   |  5 Pagesbicarbonate and carbonate by losing hydrogen ions which are now sitting around freely in the water. The hydrogen ions increase the acidity of the water. The addition of CO2 sets up a chain of events that result in these powerful little hydrogen ions being set free as the active ingredient or culprit in the damage that acids can do. Biodiversity can be threatened by increased ocean acidity. There is a huge range of harmful consequences including drops in metabolic rate or drops in immune response to other organismsRead MoreEssay on Vermicomposting is the Red Wiggler886 Words   |  4 PagesVermicomposting is a process in which red wiggler worms (eisenia fetida) decompose organic waste, such as food scraps and newspaper, in order to convert it into a natural nutrient rich fertilizer. Vermicomposter bins are very eco-friendly and are an extremely efficient way to dispose our waste as it slightly eliminates the amount of waste and pollution on earth. Vermicomposting is nature’s organic fertilizer. It also produces a rich nutrie nt full fertilizer that is much richer than outdoor compostRead MoreAnalyzing The Production Of Grapes1605 Words   |  7 Pagesdrainage. Climate: Warm locations will produce sweeter and riper fruit, therefore creating sweet wine with high alcohol content since these grapes are producing more sugar for the yeast to eat. When the climate is cool, lower temperatures maintain the acidity and make it hard for grapes to ripen. Soil: Dry, arid soil is critical since grapes don’t do well in rich, organic soils. If wines receive a large amount of nutrients, they go vegetative which is when grape veins stop producing grapes. Drainage:Read MoreEssay on Acid Rain and its Impact879 Words   |  4 Pagesscale is composed of values starting from zero, the most acidic, to 14.0, the most alkaline. (EPA USA, 2014) While regular rain has a pH value of around 5.6, acid rain has a pH value of around 4.0. The highest level of acidity of rain ever recorded was identical to the acidity of lemon juice, which is enough to irritate the human skin. (Andrei, 2012) Most acid based chemistry often happens in water because the di hydrogen oxide is capable of being a base, accepting a proton from an acid, or being

Unit 7 Assignment Essay - 1076 Words

Unit 7 Assignment Nicole Cisco Kaplan University CS204: Professional Presence Dr. McCoy July 2, 2014 Introduction Special Educators are greatly needed in our school systems all over the United States. It takes a special person to be a Special Educator. In most jobs you are in need of patience, but with this career a requirement is patience. Some people are cut out for this career and some are not. Emotionally and physically this job can take a toll on someone. In this paper I will discuss what exactly is a Special Educator, what education is needed to become one, salary, job outlook, and work environment. I have also interviewed a Special Educator and I will discuss how she feels about being†¦show more content†¦The lowest 10% earned about $36,740 and the top 10% earned about $87,390. Special Educators typically have a higher salary than a general education teacher. Work Environment The work environment for a Special Educator is in a public, magnet, private and charter schools. Some can also work in preschools. Many work the traditional 10 month school year with two months off during the summer months. Some may opt to work with special summer programs. It is not uncommon for a Special Educator to work in residential facilities, hospitals and student homes. They also can teach the child’s parents methods and ways to help the child develop skills. This career can be highly rewarding but also extremely emotionally and physically draining. This is a reason why there are not many Special Educators. Job Outlook The United States Department of Labor states that â€Å"employment of special education teachers is projected to grow 6 percent from 2012 to 2022, slower than the average for all occupations. However, overall demand will be driven by increasing enrollment and continued need for special education services.† With the advance screening and the identification of different disabilities of children are expected to increase the demand for this career. But overall increase will depend on the government’s funding. Interview I interviewed my sister, Gina O’Connor. She has been a SpecialShow MoreRelatedEssay on Unit 7 Assignment625 Words   |  3 PagesUnit 7 Assignment CJ230-02: Criminal Law for Criminal Justice Instructor: Prof Castiglione Lorraine Lopez May 5th, 2013 In this essay, I will be exploring the differences between state and federal jurisdiction in criminal prosecutions of murder with respect to crimes against persons. In the United States, both the states and the federal government have authority to prosecute criminal offenses.   The federal government and each state have its own, court system, criminal statutes, prosecutorsRead MoreUnit 7 Assignment Interpersonal Communication Kaplan University864 Words   |  4 PagesUnit 7 assignment Claudia Garcia From the interaction, does it seem to you that Alan is actively listening? Why or why not? From the interaction, it is obvious that Alan is not actively listening. First, he is not being mindful. According to Wood (2010), â€Å"mindfulness is being fully present in the moment†. In the interviews, Alan looks anxious to finish and seems to have many thing in his mind that do not allow him to be completely present. Second, he is not being person-centered (Wood, 2010). ForRead MoreUnit No: 7 Assignment 2 Business Strategy Higher National Certificate in Business Year 22794 Words   |  12 PagesLeadership Styles 6 TASK 2 7 Internal Resources 7 External Resources 8 TASK 3 10 Targets 10 Time-scales 11 Monitor and Control 12 BIBLIOGRAPHY 14 Select two distinctly different organisations from the FTSE 100 and consider the following requirements: TASK 1 Contrast each organisation relating to the culture, organisational features and leadership style: In this assignment the choice has been made to use Tesco Plc, this organisation was original identified in Assignment 1 and is a differentRead More2121 unit information1576 Words   |  7 PagesETF2121/ETF5912 Data Analysis in Business Unit Information – Semester 1 2014 Coordinator and Lecturer - Weeks 7-12: Associate Professor Ann Maharaj Office: H5.86 Phone: (990)32236 Email: ann.maharaj@monash.edu Lecturer - Weeks 1-6: Mr Bruce Stephens Office: H5.64 Phone: (990)32062 Email: bruce.stephens@monash.edu Unit material: No prescribed textbook Unit Book: available on the Moodle site. Exercises: available on the Moodle site. Software: EXCEL. Recommended Reference Books BerensonRead MoreRandom1474 Words   |  6 PagesPurpose The purpose of this assignment is to increase self-awareness of the student by analyzing personal nutritional intake and activity routine throughout the course. In turn, the student will be able to help others modify their diet and activity, and improve overall wellness. An examination of a personal food and activity assessment will provide the student with essential data from which to change their health and wellness behaviors. Course Outcomes This assignment enables the student to meetRead MoreDocument Pt1420 Essay1391 Words   |  6 PagesUnit 9: Functions Course Objectives Covered by this Unit * CO8: Apply techniques to write functions in programs. Unit Learning Outcomes * LO32: Describe the usefulness of functions in computer programs. * LO33: Write functions using pseudocode/flowcharts. * LO34: Differentiate between the various functions created for use in computer programs. * LO35: Write input validation loops and validation functions to check accuracy of input data. Key Concepts * Structures ofRead MoreAssignment 5-11084 Words   |  5 Pagesoperating income being 10% of revenue. With the current table design as is, it will cost the company $392,500 to produce 200 tables. To calculate the cost per unit one would take the total cost $392,500 and divide it by the 200 tables, which equals $1,962.50 per table. However, the target cost per unit is $1,800 meaning that the actually cost per unit is higher than the company was expecting. Therefore, value engineering is needed to help reduce costs, but still have good quality. Since the current costsRead MoreStrategic Information Management807 Words   |  4 PagesCMI Level 7 Diploma: Unit 7004 Main Assignment Introduction: The following assignment explores the importance of using information to inform and support strategic decision making to achieve organisational goals and objectives as set out by unit learning outcomes (LO) pertaining to this unit 7004. These four learning outcomes are to: LO1: Be able to understand the impact of management information on decision making; LO2: Be able to understand the importance of information sharing within the organisation;Read MoreDocx949 Words   |  4 Pagesmaterial ESP Handouts NorthStar 3 – Reading and Writing (3rd edition) 6. Lab Practice 2 sessions 7. Weekly Guide: Week 1 2 Session 1 ESP Unit 01: Information Technology - Handout 1 HW: NorthStar 3 Unit 1: The World of Advertising (pp 01- 10) Unit 02: Construction - Handout 2 HW: NorthStar 3 Unit 03: Going to Extremes Sports and Obsession (pp 3948) Unit 03: Engineering 3 4 Vocabulary and Reference Introduction Review - Introduction to Reading Skills Read MoreStrategic Management and Leadership Skills1089 Words   |  5 PagesBTEC assignments 2011  ©LAHE This assignment is a part/whole unit assessment activity BTEC – Level 7 Advanced Professional Diploma in Management Studies Assignment Brief UNIT TITLE: Developing Strategic Management and Leadership skills Assignment: Tutor: Date Set: Date of Submission: Instructions: Mr Tayo Tewogbade March 2011 17th April, 2011 Answer all questions Learning outcomes and criteria covered by this assignment 1. Understand the relationship between strategic management and leadership

Pharmacy Free Essays

I. Professionalism is an important aspect to being a Pharmacist or Pharmacy tech and must not be forgotten. A. We will write a custom essay sample on Pharmacy or any similar topic only for you Order Now Professionalism as Pharmacy Technician is based off of one’s appearance, attitude and one work ethnics. II. Having a professional appearance in the business of pharmacy is important to practice. B. Example, â€Å"Understanding how to appropriately appear, act and identify yourself as a regulated pharmacy professional is an important aspect to embracing professionalism. † (Alberta) C. Also, starting off with a professional look as you start in this career can benefit you in the long run. D. Plus, â€Å"wear appropriate identification showing name and appropriate title†. (State) III. Courteous with the customers and your fellow employees is important ethnic to have in pharmacy. E. Such as, â€Å"Introducing yourself to a patient, when receiving a prescription or helping a patient in any setting should be one of the first steps to a successful and professional interaction. † (Alberta) F. In addition, having an polite attitude with everyone, no matter the person, in the work place is very important. G. Lastly, having a good moral as an employee. IV. Being a Pharmacy Technician you may be suspected to more multiple tasks for the Pharmacist. H. Like, a Pharmacy Technician will be doing a variety of jobs that are supervised by the Pharmacist, whether it is filling prescription or stocking. I. For example, in a Pharmacy things may be repeated multiple times, so the Pharmacy Technician will be expected to perform the exact same way they did the first time. J. With this in mind, the Pharmacy Technician is just as in important as the Pharmacist themselves. V. Given these points, professionalism in a Pharmacy Technicians line of skill is very important to the everyday job. How to cite Pharmacy, Essay examples

Performance of Employees in MNC Malaysia-Free-Samples-Myassignment

Question: Discuss about the Impact of Training and Development on Employee's performance in MNC Malaysia. Answer: Introduction The research is conducted to evaluate the impact created by the training and development sessions on the performances of employees working in various multinational companies in Malaysia. The training and development programs have helped in enhancing the efficiency of recruitment and selection processes and allowed them to perform to their potential as well. (Anitha 2014). In Malaysia, the multinational organisations have provided training and development to workers for promoting growth and development and ensured more productivity, sales and profit generation too. Research aim The researchs major aim is to evaluate the effects created by training and development on the performances of workers of the multinational companies in Malaysia. Research objectives To assess the impact of training and development of the performances of workers of multinational companies in Malaysia To evaluate the most suitable approaches for enhancing the performances of workers To assess the various methods for monitoring the performances of workers within the Malaysian multinational companies To recommend relevant measures for managing training and development sessions and create positive impact on the performances of workers Research questions What impact is created by training and development on the performances of workers of Malaysian multinational companies? How can the training and development enhance the productivity of multinational organisations in Malaysia? What are the different kinds of ways or approaches for monitoring the performances of workers of Malaysian multinational companies? What are the suitable measures recommended for management of training and development and improve workers' performances and organisational productivity? Literature review The most important assets of the company are employees within the multinational companies of Malaysia. The productivity and reputation of employees are dependent upon the performances of employees and it can be managed through proper training and development provided to them (Bello 2012). Definition of key concept Strategic leadership The strategic leadership is an essential aspect that focuses on the ability to influence individuals and allow them to make decisions in an effective manner. This would contribute to the overall success of the organization as well as maintain good financial stability. The strategic leadership provides a direction to ensure proper growth and development of the company. To manage changes, the business executives need proper skills and knowledge to formulate the strategies and implement those for successful business planning (Anitha 2014). To manage changes and ambiguity, strategic leadership is essential for providing a sense of direction to employees as well as develop ownership and alignment within the groups of individuals to manage changes easily (Bashir and Long 2015). Work performances of employees Work performances are needed to be monitored consistently for checking whether the employees have managed to fulfill the requirements and criteria or not to achieve the organisational goals and objectives. In case the employees lacked certain skills, knowledge and expertise, it is the duty of the human resource management department to provide them with training sessions so that their skills and knowledge are improved, and they can work with much more commitment and dedication (Cherian and Jacob 2013). Training and development Training and development sessions can be provided through case studies illustration, classroom lectures, role-playing, simulations as well as computer based training programs (Elnaga and Imran 2013). The multinational companies in Malaysia must assess and identify the training and developmental needs of employees and understand that each of them has different types of needs and preferences, which are needed to be met carefully for progressing in their professional career (Ford 2014). Thus, the training and development are important for both improving the performances of employees and organisational development (Giuliani and Macchi 2013). Training and development could bring several benefits such as enhanced productivity and less supervision required. The employees performances are monitored to identify weaknesses and reduce the turnover of employees, increase consistency, lift up team spirits, enable optimum utilisation of resources and decrease time of learning. The informal training and development can help in learning through feedbacks and enable social interaction between the organisation and employees working there (Jehanzeb, Rasheed and Rasheed 2013). Critical review of Theories and models Contingency theory Thecontingency theoryis an effective theory used within the Malaysian multinational companies for leading the organisation in the right direction and make proper decisions. Here, contingent means dependent and the organization manages its business operations and processes based on the external and internal conditions (Kennett 2013). The leaders apply their own style of leadership in the right situations to assess the environment within which the company operates and ensure delivering good quality products and services to customers. With the help of managerial skills, they can utilize information technology to improve the performances of employees through necessary training and development (Kooij et al. 2013). Trait theory The trait theory is another important approach, which can enhance the efficiency of training and development provided to individuals working within the multinational companies of Malaysia. The trait theory is used to evaluate the behaviour of employees and their emotions and check, whether they are feeling interested in working for the company properly or not. The trait theory fosters the effectiveness of leadership across various groups of the organisation, focus on the behaviors of employees, and motivate them to perform to their potential (Long, Perumal and Ajagbe 2012). A Great Man theory TheGreat Man theoryis another appropriate theory, which shows the skills and abilities of leaders to act as a hero and influence others through their personal charisma, wisdom, intelligence. (Beh and Loo 2013). The great man theory of leadership has showed that leaders are born with necessary attributes, which have made them apart from others and these traits or behaviors are responsible for determining the authority and position of the organization too (Bello 2012). Summary of theories and models Theory and model Description Strengths Weaknesses Source Contingency The leaders apply their own style of leadership. Applying own leadership skills and expertise Lack of employees opinions (Bello 2012) Trait Fosters leadership effectiveness across various groups. Giving a proper direction to employees. Few groups remain out of focus as leaders may not be able to give equal attention to every groups (Anitha 2014) Great man theory The great man theory of leadership has showed that leaders are born with necessary attributes and determine the authority and position of organization The leaders care for the employees and promote diversity. Leaders often become aggressive of bringing out the best from employees (Elnaga and Imran 2013) Empirical studies The sample size is 200 respondents and the variable, which has been used is abc. Based on the findings, it could be understood that workers link the training and development sessions provided to customers with the organizations production level and more commitment. The training and development is related to the earnings per share and return on investments done for the training provided to workers. Summary of variables Variables Source 1. Vision Vision is to enhance organisational productivity through enhancement of workers performances (Ford 2014) 2. Core competency Allocating resources properly and manage differentiating of products. (Lee, Lee and Kang 2012) 3. Strategic direction Leading the employees in right direction and making them skilful through training and development. (Kennett 2013) H1: Training and development has created a positive impact on the performances of workers. H2: Training and development encourages motivation of employees. H3: The training and development has influenced the behaviors of employees and made them work with dedication. Conceptual framework Research design and methodology Research philosophy There are three different types of philosophies including the positivism, interpretivism and realism (Manzoor 2012). The research is primary, and so there is involvement of both quantitative and qualitative data. Interpretivism does not consider the scientific approaches, and so the assumptions made are subjective, which was needed to be objective. The quantitative data has been gathered through questionnaires distributed to customers, and so positivism research philosophy is considered here as the most effective (Mohamed et al. 2013). Thus, here the positivism research philosophy is the most effective among the other philosophies of research. Research design and strategy The three different kinds of research designs such as the exploratory, explanatory and descriptive. The exploratory research design defines the initial research and presents it with the help of theoretical data. It is useful for making observations and understands more about the research topic, which can help in carrying out the research in future as well. The existing theories and concepts can be used as well for developing an initial framework to conduct the research in the future. The explanatory research design determines the cause and effect of research and generate ideas about how things are communicated and are linked with each other (Ramayah, Ahmad and Hong 2012). The descriptive research design, as the name suggests is useful for exploring the various concepts of the research along with its variables in details. Thus, it could be understood that the descriptive research design focused on the what' and how' rather than why' (Salleh and Omar 2013). The dependent variable here is the performances of employees, and it is dependent upon the training and development, which is the independent variable (Sethi 2012). Thus, descriptive research design has helped in creating a positive impact of the independent variable on dependent variables for improving the performances of employees and contribute to the organisational efficiency. Data collection method The collection of data includes both primary and secondary data. The primary data includes both qualitative and quantitative data. The quantitative data is gathered in the form of responses and feedbacks of customers, which have been derived from the distribution of survey questionnaires to them. On the other hand, the managers of few of the multinational companies have been allowed to take part in the interview where they were asked certain questions and the answers provided are considered as qualitative data (Singh and Mohanty 2012). The secondary data is collected by following the secondary sources like journals, articles, blogs, newspapers, magazines and the internet web sites. The focus groups consist of a group of individuals who provide their responses and feedbacks for conducting a market research regarding the topic of the impact of training and development of performances of employees (Anitha 2014). The members of the focus group are selected properly for gaining their appropriate and authoritative responses in an effective manner. To check whether the questionnaires are reliable enough or not, the Cronbachs Alpha measurement had been used for making it easy for the respondents to answer the questions and it had been recorded as 0.907 (Bashir and Long 2015). It is above the normal reliability coefficient, so few changes are needed to be made though. Target or total population The targeted population is the number of employees working within Malaysian multinational companies. 500 questionnaires had been provided to the employees of the organisation, though nearly 200 had been returned. 11 questionnaires came back without any thing filled in those and 189 were used properly (Beh and Loo 2013). This resulted in delivering a yield of 95 percent while the partially filled up questionnaires had been returned to them as well. Sample size and Sampling method The sample size has been chosen as 200 employees and 50 managers of the most established multinational companies in Malaysia. For quantitative data, the sampling method is chosen as probability sampling method whereas for gathering qualitative samples, the non-probability sampling technique is more effective. The non-probability sampling method consists of purposive, convenient, availability and quota sampling (Bello 2012). The convenient sampling method provides the managers with a suitable time when they can be present and take part in the interview session to answer several questions asked by the researcher. The random probability sampling method helps in choosing random samples and distributes survey questionnaires to them for collecting quantitative data (Cherian and Jacob 2013). Data instrument The questionnaires are used along with Liker scale, which provides a range from 1 to 5. Variable Sub-Variable SA A N D SD Source Training 1. Gain practical skills 2. Knowledge acquisition 3. Enhance strengths 4. Makes employees handle critical situations (Bello 2012) Development 1 Training sessions 2 Role playing 3 Growth 4 Organisational success (Manzoor 2012) Leadership 1 Influences employee behaviour 2 Strengthening organisational position 3 Increase in organisational production 4 Guiding employees in right direction (Sethi 2012) Employee performance 1 Reward management system 2 Good working conditions 3 Training and development 4 Good work culture (Ramayah, Ahmad and Hong 2012) Accessibility and ethical issues The accessibility issues include lack of availability of managers, employees at the same time, which may make the researcher visit several places, and that is quite time-consuming. The questionnaires must be provided to respondents with a consent letter, and those should be tangible rather than being virtual (Elnaga and Imran 2013). There could be ethical issues in case the respondents do not want to participate. A power failure or network disruption could lead to loss of data and information. The research was conducted for academic purposes and not for gaining any commercial benefits (Ford 2014). Data analysis plan The data analysis has been done with the help of SPSS tool which can represent the data in the form of graphs and tables for making the researcher understand easily about the responses of individuals regarding the impact of training and development on performances of employees. The various ways of analysing data are reliability test, normality test, descriptive analysis, regression analysis, correction analysis and validity test (Giuliani and Macchi 2013). Analysis Reasons Source Normality test To check whether the data set is properly structured or not and how random variables are distributed (Salleh and Omar 2013) Reliability test For checking the data and information gathered are valid or not. (Sethi 2012) Descriptive It is used to manage proper design and ensure strategic formulation if research. (Manzoor 2012) Correlation Manage learning for linear association between two variables. (Mohamed et al. 2013) Regression For ensuring development and testing of software and manage changes in configuration, patches, software developments, etc. (Ramayah, Ahmad and Hong 2012) Research limitations Time and cost are the major constraints of the research while the respondents may also not provide the answers without bias. There are language barriers too, which can create difficulties for individuals to understand the questionnaires and for that, they may even skip few questions. Though the research has been completed within the allocated time frame, still some additional time and money are needed for completing the research in a much more detailed manner in the future too (Gunnigle, Lavelle and Monaghan 2013). Research timeline Activities February March April May June July Selection of topic Secondary collection of data Constructing the research layout Literature review Development of research Plan Selection of Appropriate Research Techniques Primary data collection Analysis Interpretation of Data which are collected Conclusion Development of Draft Final Work submission References Anitha, J., 2014. Determinants of employee engagement and their impact on employee performance.International journal of productivity and performance management. Bashir, N. and Long, C.S., 2015. The relationship between training and organizational commitment among academicians in Malaysia.Journal of Management Development,34(10), pp.1227-1245. Beh, L.S. and Loo, L.H., 2013. Human resource management best practices and firm performance: A universalistic perspective approach.Serbian Journal of Management,8(2), pp.155-167. Bello, S.M., 2012. Impact of ethical leadership on employee job performance.International Journal of Business and Social Science,3(11). Cherian, J. and Jacob, J., 2013. Impact of self efficacy on motivation and performance of employees.International Journal of Business and Management,8(14), p.80. Elnaga, A. and Imran, A., 2013. The effect of training on employee performance.European Journal of Business and Management,5(4), pp.137-147. Ford, J.K., 2014.Improving training effectiveness in work organizations. Psychology Press. Giuliani, E. and Macchi, C., 2013. Multinational corporations economic and human rights impacts on developing countries: a review and research agenda.Cambridge Journal of Economics,38(2), pp.479-517. Gunnigle, P., Lavelle, J. and Monaghan, S., 2013. Weathering the storm? Multinational companies and human resource management through the global financial crisis.International Journal of Manpower,34(3), pp.214-231. Jehanzeb, K., Rasheed, A. and Rasheed, M.F., 2013. Organizational commitment and turnover intentions: Impact of employees training in private sector of Saudi Arabia.International Journal of Business and Management,8(8), p.79. Kennett, G., 2013. The impact of training practices on individual, organisation, and industry skill development.Australian Bulletin of Labour,39(1), p.112. Kooij, D.T., Guest, D.E., Clinton, M., Knight, T., Jansen, P.G. and Dikkers, J.S., 2013. How the impact of HR practices on employee well?being and performance changes with age.Human Resource Management Journal,23(1), pp.18-35. Lee, S.M., Lee, D. and Kang, C.Y., 2012. The impact of high-performance work systems in the health-care industry: employee reactions, service quality, customer satisfaction, and customer loyalty.The Service Industries Journal,32(1), pp.17-36. Long, C.S., Perumal, P. and Ajagbe, A.M., 2012. The impact of human resource management practices on employees turnover intention: A conceptual model.Interdisciplinary Journal of Contemporary Research in Business,4(2), pp.629-641. Manzoor, Q.A., 2012. Impact of employees motivation on organizational effectiveness.Business management and strategy,3(1), p.1. Mohamed, A.F., Singh, S., Irani, Z. and Darwish, T.K., 2013. An analysis of recruitment, training and retention practices in domestic and multinational enterprises in the country of Brunei Darussalam.The International Journal of Human Resource Management,24(10), pp.2054-2081. Ramayah, T., Ahmad, N.H. and Hong, T.S., 2012. An assessment of e-training effectiveness in multinational companies in Malaysia.Journal of Educational Technology Society,15(2), p.125. Salleh, M.S. and Omar, M.Z., 2013. University-industry collaboration models in Malaysia.Procedia-Social and Behavioral Sciences,102, pp.654-664. Sethi, S.P., 2012.Multinational corporations and the impact of public advocacy on corporate strategy: Nestle and the infant formula controversy(Vol. 6). Springer Science Business Media. Singh, R. and Mohanty, M., 2012. Impact of training practices on employee productivity: A comparative study.Interscience Management Review,2(2), pp.87-92.

Managing Change The Case of FastLink Logistics Company

Introduction Contextual Information Cut-throat competition, technological advances, geopolitical realignments and other related pressures are combining with concerns for security, shifting customer demands, expansion urges and organizational governance to generate momentous pressure for organizational change (Howard, 1994). Current literature as demonstrated by Kotter (2007) reveals that organizations need to continually change and reinvent their strategies, structures, processes and culture to remain relevant as well as maintain competitive advantage.Advertising We will write a custom essay sample on Managing Change: The Case of FastLink Logistics Company specifically for you for only $16.05 $11/page Learn More But as observed by McGahan (2004), the change process itself need to be planned beforehand and aligned to the business strategy and objectives if it is to achieve success. The capacity of an organization to plan and implement the change process is therefore fundamental for success. By presenting a case of the current challenges facing FastLink Logistics Company, this paper will focus on providing an outline through which the underlying challenges can be adequately addressed by initiating a change process. Headquartered in Boston, MA, FastLink Logistics has been in operation for the last 20 years, and has consistently maintained a leadership position in the industry judging from its financial returns and competitiveness. An interview with the company’s operations manager revealed that the company operates a fleet of 3000 trucks and 10 cargo airplanes for purposes of transporting goods to various destinations across the U.S. and internationally. From the beginning of the current financial year, however, the company’s management has been receiving sustained customer complaints regarding delayed deliveries of their orders, especially from truck drivers. Indeed, some of FastLink’s traditional customers have opted to look for other logistics companies who keep their word on deliveries, implying that profits for FastLink Logistics have been on a downward trend. The management, having studied all the facts, identified massive paperwork in cargo clearing departments and irresponsible behaviour on the part of truck drivers, who engage in personal business while performing official duties. Upon holding several consultative meetings, the management decided to undertake a change process that will automate the clearing departments and install remote sensors on their trucks to monitor their movements and timeliness. The intended change process, however, is likely to experience some challenges, especially from employees who may oppose the intended automation of duties for fear of being rendered redundant. Still, truck drivers may feel that the intended introduction of remote sensors on their trucks may impinge on their privacy, hence perceive the new system negatively. Overall, the change proces s may be resisted by employees since it requires dramatic shifts in business processes and employee roles (Suntano et al., 2008). The management, therefore, must come up with strategies that ensure employee participation, commitment and identification to the change process so as to achieve success. In line with the above, FastLink’s management decides to enrol the services of a consultant to prepare a project feasibility study that could be effectively used to manage the change process.Advertising Looking for essay on business economics? Let's see if we can help you! Get your first paper with 15% OFF Learn More Project Feasibility Study for FastLink Logistics Company The Project Scope Greer Conradi (2009) observes that â€Å"†¦the feasibility study usually refers to an assessment of the product/project against technical, operational, financial and social/political criteria† (p. 357). Academics and practitioners are in agreement that recognizing the challenges facing an organization and justifying the need for change must form the initial step of a system change effort (Suntano et al., 2008). Section A of this report demonstrates that FastLink is currently being faced with challenges arising from slower business processes and inability of some employees, particularly truck drivers, to identify with the values of the company. These challenges have caused the company to lose its traditional customers to competitors due to late delivery of orders, implying that the company’s profitability and competitive advantage in the market have been negatively affected. This particular feasibility study, hereafter identified as PFS, will therefore aim to come up with ways to balance business processes and technology constraints facing the firm so as to select a cost-effective solution. More importantly, the PFS will also involve matching the new system to organizational objectives in terms of deliverables, ability to meet customersâ⠂¬â„¢ requirements, efficient utilization of resources, budgetary allocations and time-frames. The PFS will be presented in the form of a short report. The Current Analysis FastLink logistics has for a very long time employed a manual process in its operations across all the offices located in the U.S. and abroad. This implies that the work environment has been largely paper-based and personnel-intensive. It is also imperative to note that FastLink’s working environment has been largely distributed over expansive geographical areas due to the nature of the transportation business. The advantages derived from the above working methodology may in fact be minimal as opposed to the disadvantages. In terms of advantages of the ‘status-quo’, it is important to note that manual processes of doing business in a way motivates employees to offer more, not mentioning that they are beneficial in aligning members of staff to organizational objectives and strategies (McGahan, 2004). A paper-based working environment also implies that information can be retrieved from the cabinets anytime without undue regard to other externalities such as the availability of power to run the machines, computer viruses, and end-user capabilities. In terms of the disadvantages arising from the current business processes, it is evident that FastLink has been losing, productively, due to delay occasioned by the tedious paper-based working environment and centralized information architecture.Advertising We will write a custom essay sample on Managing Change: The Case of FastLink Logistics Company specifically for you for only $16.05 $11/page Learn More Preliminary observations reveals that the distributed information architecture coupled with lax rules are to blame for the truck drivers’ unbecoming behaviour by virtue of the fact that critical information aimed at necessitating effective order deliveries to customers is either delayed due to the manual operational processes, or the information does not get to the intended recipients at all due to lax operational rules. Another problematic area for the company is the fact that it has to employ a large number of employees to do the paperwork needed to necessitate order deliveries, implying that the company’s wage bill may exceed profitable limits. These disadvantages, according to preliminary observations, are to blame for the company’s continued dip in profitability and competitive advantage within the logistics industry. According to Davies (1994), these challenges are functional in nature owing to the fact that they hinder effective work-flow processes for the company, thus they demand functional solutions. Benefits Pitfalls of the Proposed System The next stage of designing a project feasibility study, according to Greer Conradi (2009), is to develop specific objectives and limits of the proposed system. Here, it is proposed that the company redesig n and automate its database management system for the obvious advantages of faster and better customer service as well as ensuring the distributed use and processing of order information. Automated work systems, according to Howard (1994), not only simplify and streamline work processes, but they also enhance efficiency by curtailing excessive use of an organization’s scarce resources. The proposed remote sensors to be installed on trucks will go a long way to ensure that truck drivers follow their routes in the process of delivering orders to customers, and the orders are delivered on a timely basis. However, financial resources must be channelled to purchase the needed automation hardware and software as well as the remote sensors. The decisions to automate the offices and install remote sensors on trucks will most probably be met with resistance from members of staff who may fear loosing their jobs or who may argue that their privacy is being impinged on. Here, Suntano et al (2008) advises that the company should take an all-inclusive approach to enable employees participate in the change process; hence offer their views, fears and expectations as concerns the intended change. In addition, the management should exercise an open-door policy, whereby employees should be encouraged to raise any underlying issues and seek clarifications to better understand the proposed change.Advertising Looking for essay on business economics? Let's see if we can help you! Get your first paper with 15% OFF Learn More According to Davies (1994), involving employees and effectively answering their concerns in any change process is advantageous since it minimizes resistance during the implementation process, not mentioning that it facilitates employees to identify more with the change process once it is operationalized. Alternatives Companies in the 21st century are increasingly faced with the dilemma of whether to automate their operations or to continue with paper-based working environment (Alkuwaiti, 2010). In the present case, one of the viable alternatives would be to recruit more human resources to clear the backlog, hence necessitate timely delivery of orders to customers. Another alternative would be to enlist the services of security firms to escort trucks so that drivers do not engage in personal business during official working hours. The company may also consider investing in telecommunications to facilitate a more distributed information infrastructure. Assessment The assessment of any viable change process or alternatives must be evaluated against a backdrop of risk management controls, ability to meet fundamental objectives of the project’s attention, program needs and costs, intensity of effort, time-scale, security features, and flexibility for future modification and expansion, among others (Kotter, 2007; Bryce, 2011). It is indeed true that the proposed automated process may in the short-term be costly for the company in terms of purchasing the needed hardware and software as well as training staff members to operate the automated systems. In the long-term, however, the company will largely benefit from enhanced customer satisfaction, improved sales and reduced overhead costs. The alternative of employing more members of staff to clear the backlog may not be tenable in these circumstances, especially when the company is working on new modalities that will enable it to return to profitability and maintain competitive advantage. The time-scale needed f or implementing automated systems and installing the remote sensors may indeed be minimal when it is compared to the time-scale and resources needed to advertise for positions, recruit, orient and train new members of staff. According to Howard (1994), companies must always be on the lookout for proposals that enhance value creation as well as offer viable solutions to the problems that triggered the change process. In this perspective, the proposed system change should be recommended over the other stated alternatives. Automation of business process and introduction of remote sensors for trucks seem the only way to go for FastLink Logistics Company if it has to overcome its present challenges. Lastly, it is indeed true that automated systems can be expanded or modified to meet future needs and expectations (Suntano et al., 2008). The same cannot be said of other alternatives such as utilizing security firms to make the company drivers toe the line. List of References Alkuwaiti, A. J. (2010). The Project Book: A Simple and Direct Approach to Project Management. New York, NY: Create Space. Bryce, T. (2011). The Elements of a Good Feasibility Study. Web. Davis, S. M. (1994). Attempting Major Change? 10 Pitfalls to Avoid – And How. Human Resource Planning, Vol. 7, Issue 4, pp 175-188. Greer, D., Conradi, R. (2009) Software Project Initiation and Planning – An Empirical Study. IET Software, Vol. 3, Issue 5, pp 356-368. Howard, A. (1994). Diagnosis for Organizational Change: Methods and Models. New York, NY: The Guilford Press. Kotter, J. P. (2007). Leading Change. Harvard Business Review, Vol. 85, Issue 1, pp 96-103. McGahan, A. M. (2004). How Industries Change. Harvard Business Review, Vol. 82, Issue 10, pp 86-94. Suntano, J., Kankanhalli, A., Tay, J., Raman, K. S., Tan, B. C. Y. (2008). Change Management in Interorganizational Systems for the Public. Journal of Management Information Systems, Vol. 25, Issue 3, pp 133-175. Wischnevsky, J. D. (2007 ). Change as the Winds Change: The Impact of Organizational Transformation on Firm Survival in a Shifting Environment. Organizational Analysis, Vol. 12, Issue. 4 pp 361-377. This essay on Managing Change: The Case of FastLink Logistics Company was written and submitted by user Ian U. to help you with your own studies. You are free to use it for research and reference purposes in order to write your own paper; however, you must cite it accordingly. You can donate your paper here.

Linear Solution Essays

Linear Solution Essays Linear Solution Essay Linear Solution Essay CHAPTER 8 Linear Programming Applications Teaching Suggestions Teaching Suggestion 8. 1: Importance of Formulating Large LP Problems. Since computers are used to solve virtually all business LP problems, the most important thing a student can do is to get experience in formulating a wide variety of problems. This chapter provides such a variety. Teaching Suggestion 8. 2: Note on Production Scheduling Problems. The Greenberg Motor example in this chapter is largest large problem in terms of the number of constraints, so it provides a good practice environment. An interesting feature to point out is that LP constraints are capable of tying one production period to the next. Teaching Suggestion 8. 3: Labor Planning Problem- Hong Kong Bank of Commerce. This example is a good practice tool and lead-in for the Chase Manhattan Bank case at the end of the chapter. Without this example, the case would probably overpower most students. Teaching Suggestion 8. 4: Ingredient Blending Applications. Three points can be made about the two blending examples in this chapter. First, both the diet and fuel blending problems presented here are tiny compared to huge real-world blending problems. But they do provide some sense of the issues to be faced. Second, diet problems that are missing the constraints that force variety into the diet can be terribly embarrassing. It has been said that a hospital in New Orleans ended up with an LP solution to feed each patient only castor oil for dinner because analysts neglected to add constraints forcing a well-rounded diet. Alternative Examples Alternative Example 8. 1:  Ã‚  Natural Furniture Company manufactures three outdoor products, chairs, benches, and tables. Each product must pass through the following departments before it is shipped: sawing, sanding, assembly, and painting. The time requirements (in hours) are summarized in the tables below. The production time available in each department each week and the minimum weekly production requirement to fulfill contracts are as follows: | | |Minimum | | |Capacity | |Production | |Department |(In Hours) |Product |Level | |Sawing |450 |Chairs |100 | |Sanding |400 |Benches |50 | |Assembly |625 |Tables |50 | |Painting |550 | | | |Hours Required |Unit | |Product |Sawing |Sanding |Assembly |Painting |Profit | |Chairs |1. 5 |1. 0 |2. 0 |1. 5 |$15 | |Benches |1. 5 |1. 5 |2. 0 |2. 0 |$10 | |Tables |2. 0 |2. 0 |2. 5 |2. 0 |$20 | The production manager has the responsibility of specifying production levels for each product for the coming week. Formulate as a linear programming problem to maximize profit. Let X1= Number of chairs produced X2= Number of benches produced X3= Number of tables produced The objective function is Maximize profit = 15X1 + 10X2 + 20X3 Constraints 1. 5X1 + 1. 5X2 + 2. 0X3( 450 hours of sawing available 1. 0X1 + 1. 5X2 + 2. 0X3( 400 hours of sanding available 2. 0X1 + 2. 0X2 + 2. 5X3( 625 hours of assembly available 1. 5X1 + 2. 0X2 + 2. 0X3( 550 hours of painting available X1+ 2. 0X2 + 2. 0X3( 100 chairs X2 + 2. 0X3( 50 benches X3( 50 tables X1, X2, X3( 0 What mix of products would yield maximum profit? Solving with computer software we get: X1= 100 chairs; X2 = 50 benches; X3 = 112. 5 tables; profit = 4250. Alternative Example 8. 2:  Ã‚  A phosphate manufacturer produces three grades of phosphate, A, B, and C, which yield profit of $40, $50, and $60 per kilogram, respectively. The products require the labor and materials per batch that are shown in the table. Each batch of Grade A phosphate yields 800kg of phosphate; each batch of Grade B phosphate yields 700kg of phosphate; and each batch of Grade C phosphate yields 800 kg. |Grade |Grade |Grade |Available | | |A |B |C |Resources | |Labor hours |4 |4 |5 |80 hr | |Raw material #1 |200 |300 |300 |6,000 kg | |Raw material #2 |600 |400 |500 |5,000 kg | Formulate as an LP problem to maximize profit. Objective function Maximize profit = 40(800)A + 50(700)B + 60(800)C Constraints Labor:4A +4B +5C( 80 Raw material #1200A + 300B +300C( 6,000 Raw material #2600A + 400B +500C( 5,000 What mix of products would yield maximize profit? Solutions To Problems 8-1. Since the decision centers about the production of the two different cabinet models, we let X1= number of French Provincial cabinets produced each day X2= number of Danish Modern cabinets produced each day Objective: maximize revenue = $28X1 + $25X2 subject to 3X1 + 2X2( 360 hours  Ã‚  (carpentry department) [pic] X1 + 1X2( 200 hours  Ã‚  (painting department) [pic]X1 + [pic] X2( 125 hours  Ã‚  (finishing department) X1( 60 units  Ã‚  (contract requirement) X2( 60 units  Ã‚  (contract requirement) X1, X2( 0 Problem 8-1 solved by computer: Produce 60 French Provincial cabinets (X1) per day Produce 90 Danish Modern cabinets (X2) per day Revenue = $3,930 8-2. Let X1= dollars invested in Los Angeles municipal bonds X2= dollars invested in Thompson Electronics X3= dollars invested in United Aerospace X4= dollars invested in Palmer Drugs X5= dollars invested in Happy Days Nursing Homes Maximize return = 0. 53X1 + 0. 068X2 + 0. 049X3 + 0. 084X4 + 0. 118X5 subject to X1 + X2 + X3 + X4 + X5 ( $250,000 (funds) X1( . 2 (X1 + X2 + X3 + X4 + X5) (bonds) or ( . 8X1 – . 2X2 – . 2X3 – . 2X4 – . 2X5 ( 0 X2 + X3 + X4( . 4 (X1 + X2 + X3 + X4 + X5) (combination of electronics, aerospace, and drugs) or –0. 4X1 + 0. 6X2 + 0. 6X3 + 0. 6X4 – 0. 4X5 ( 0 (X5 ( 0. 5X1) rewritten as –0. 5X1 + X5 ( 0 (nursing home as percent of bonds) X1, X2, X3, X4, X5 ( 0 Problem 8-2 solved by computer: $50,000invested in Los Angeles municipal bonds (X1) $0invested in Tho mpson Electronics (X2) $0invested in United Aerospace (X3) 175,000invested in Palmer Drugs (X4) $25,000invested in Happy Days (X5) This produces an annual return on investment of $20,300. 8-3. Minimize staff size = X1 + X2 + X3 + X4 + X5 + X6 where Xi = number of workers reporting for start of work at period i (with i = 1, 2, 3, 4, 5, or 6) X1 + X2 ( 12 X2 + X3 ( 16 X3 + X4 (   9 X4 + X5 ( 11 X5 + X6 (   4 X1 + X6 ( 3 All variables ( 0 The computer solution is to hire 30 workers: 16 begin at 7 a. m. 9 begin at 3 p. m. 2 begin at 7 p. m. 3 begin at 11 p. m. An alternative optimum is 3 begin at 3 a. m. 9 begin at 7 a. m. 7 begin at 11 a. m. begin at 3 p. m. 9 begin at 7 p. m. 0 begin at 11 p. m. 8-4. Let X1= number of pounds of oat product per horse each day X2= number of pounds of enriched grain per horse each day X3= number of pounds of mineral product per horse each day Minimize cost = 0. 09X1 + 0. 14X2 + 0. 17X3 subject to 2X1+ 3X2 + 1X3 ( 6 (ingredient A) [pic]X1+ 1X2 + [pic]X3 ( 2 (ingredient B) 3X1+ 5X2 + 6X3 ( 9 (ingredient C) 1X1+ 1[pic]X2 + 2X3 ( 8 (ingredient D) [pic]X1+ [pic]X2 + 1[pic]X3 ( 5 (ingredient E) X1+ X2 +X3 ( 6 (maximum feed/day) All variables ( 0 Solution: X1= 1[pic] X2= 0 X3= 3[pic] cost= 0. 87 8-5. Let E1, E2, and E3 represent the ending inventory for the three months respectively. Let RT1, RT2, and RT3 represent the reguar production for the three months and OT1, OT2, an d OT3 represent the overtime production quantities during the three months respectively. Then the formulation is: Minimize cost: 300RT1 + 300RT2 + 300RT3 + 325OT1 + 325OT2 + 325OT3 + 20E1 + 20E2 + 20E3 subject to RT1 lt; 200 June regular production RT2 lt; 200 July regular production RT3 lt; 200 August regular production OT1 lt; 15 June overtime production OT2 lt; 15 July overtime production OT3 lt; 15 August overtime production (E1 + RT1 + OT1= 195 Ending inventory from first month (E2 + E1 + RT2 + OT2= 215 Ending inventory from second month (E3 + E2 + RT3 + OT3= 205 Ending inventory from third month {All variables}? 0 Non-negativity constraints The optimal production schedule is to produce 200 each month during regular production and to use overtime to produce 10 units in July and 5 in August for a total cost of $184,975. 8-6. Let T = number of TV ads R = number of radio ads B = number of billboard ads N = number of newspaper ads Maximize total audience = 30,000T + 22,000R + 24,000B + 8,000N Subject to 800T + 400R + 500B + 100N ( 15,000 ? ( 10 R (10 ? (10 ? (10 ? + R ( 6 500B + 100N ( 800T ?, R, ? , ? ( 0 Solution: T = 6. 875; R = 10; B = 9; N = 10; Audience reached = 722,250. If integer solutions are necessary, integer programming (see Chapter 11) could be used. 8-7. Let_X1= number of newspaper ads placed X2= number of TV spots purchased Minimize cost =$925X1 + $2,000X2 subject to0. 04X1 + 0. 05X2 ( 0. 40 (city exposure) 0. 03X1 + 0. 03X2 ( 0. 60 (exposure in northwest suburbs) X1, X2 ( 0 Note that the problem is not limited to unduplicated exposure (e. g. one person seeing the Sunday newspaper three weeks in a row counts for three exposures). Problem 8-7 solved by computer: Buy 20 Sunday newspaper ads (X1) Buy 0 TV ads (X2) This has a cost of $18,500. Perhaps the paint store should consider a blend of TV and newspaper, not just the latter. 8-8. Let Xij = number of new leases in month i for j-months, i = 1, . . . , 6; j = 3, 4, 5 Minimize cost =1260X13 + 1260X23 + 1260X 33 + 1260X43 + 840X53 + 420X63 + 1600X14 + 1600X24 + 1600X34 + 1200X44 + 800X54 + 400X64+ 1850X15 + 1850X25 + 1480X35 + 1110X45 + 740X55 + 370X65 subject to:X13 + X14 + X15 ( 420 – 390 X13 + X14 + X15 + X23 + X24 + X25 ( 400 – 270 X13 + X14 + X15 + X23 + X24 + X25 + X33 + X34 + X35 ( 430 – 130 X14 + X15 + X23 + X24 + X25 + X33 + X34 + X35 + X43 + X44 + X45 ( 460 X15 + X24 + X25 + X33 + X34 + X35 + X43 + X44 + X45 + X53 + X54 + X55 ( 470 X25 + X34 + X35 + X43 + X44 + X45 + X53 + X54 + X55 + X63 + X64 + X65 ( 440 X15 + X25 + X35 + X45 + X55 + X65 ( 0. 0(X13 + X14 + X15 + X23 + X24 + X25 + X33 + X34 + X35 + X43 + X44 + X45 + X53 + X54 + X55 + X63 + X64 + X65) All variables ( 0 Solving this on the computer results in the following solution: X15 = 305-month leases in March X25 = 1005-month leases in April X35 = 1705-month leases in May X45 = 1605-month leases in June X55 = 105-month leases in July All other variables equal 0. Total cost = $677,100. As a result of this, there are 440 cars remaining at the end of August. 8-9. The linear program has the same constraints as in problem 8-8. The objective function changes and is now: Minimize cost =1260(X13 + X23 + X33 + X43 + X53 + X63) + 1600(X14 + X24 + X34 + X44 + X54 + X64) + 1850(X15 + X25 + X35 + X45 + X55 + X65) Solving this on the computer results in the following solution: X15 = 305-month leases in March X25 = 1005-month leases in April X34 = 654-month leases in May X35 = 1055-month leases in May X43 = 1603-month leases in June X53 = 103-month leases in July All other variables equal 0. Total cost = $752,950. 8-10. Let Xij = number of students bused from sector i to school j Objective: minimize total travel miles = 5XAB+ 8XAC + 6XAE 0XBB+ 4XBC + 12XBE + 4XCB+ 0XCC + 7XCE + 7XDB+ 2XDC + 5XDE + 12XEB+ 7XEC + 0XEE subject to XAB + XAC + XAE= 700 (number of students in sector A) XBB + XBC + XBE= 500 (number of students in sector B) XCB + XCC + XCE= 100 (number of students in sector C) XDB + XDC + XDE= 800 (number of students in sector D) XEB + XEC + XEE= 400 (number students in sector E) XAB + XBB + XCB + XDB + XEB ( 900 (school B capacity) XAC + XBC + XCC + XDC + XEC ( 900 (school C capacity) XAE + XBE + XCE + XDE + XEE ( 900 (school E capacity) All variables ( 0 Solution: XAB= 400 XAE= 300 XBB= 500 XCC= 100 XDC= 800 XEE= 400 Distance = 5,400 â€Å"student miles† 8-11. Maximize number of rolls of Supertrex sold = 20X1 + 6. 8X2 + 12X3 – 65,000X4 whereX1= dollars spent on advertising X2= dollars spent on store displays X3= dollars in inventory X4= percent markup subject to X1 + X2 + X3 ( $17,000 (budgeted) X1( $3,000 (advertising constraint) X2( 0. 05X3 (or X2 – 0. 05X3 ( 0) (ratio of displays to inventory) [pic] (markup ranges) X1, X2, X3, X4 ( 0 Problem 8-11 solved by computer: Spend $17,000 on advertising (X1). Spend nothing on in-store displays or on-hand inventory (X2 and X3). Take a 20% markup. The store will sell 327,000 rolls of Supertrex. This solution implies that no on-hand inventory or displays are needed to sell the product, probably due to an oversight on Mr. Kruger’s part. Perhaps a constraint indicating that X3 ( $3,000 of inventory should be held might be needed. 8-12. Minimize total cost = $0. 60X1 + 2. 35X2 + 1. 15X3 + 2. 25X4 + 0. 58X5 + 1. 17X6 + 0. 33X7 subject to 295X1 + 1,216X2 + 394X3 +358X4 + 128X5+ 118X6 + 279X7 ( 1,500 295X1 + 1,216X2 + 394X3 +358X4 + 128X5+ 118X6 + 279X7 ( 900 .2X1 + 121. 2X2 + . 4. 3X3 + 3. 2X4 + 3. 2X5+ 14. 1X6 + 2. 2X7 ( 4 16X1 +1,296X2 + . 4. 9X3 + 0. 5X4 + 0. 8X5+ 1. 4X6 + 0. 5X7 ( 50 6X1 + 81X2 + 74X3 + 83X4 + 7X5+ 14X6 +  8X7 ( 26 22X1 + 28X5 + 19X6 + 63X7( 50 All Xi ( 0 Problem 8-12 solved by computer: The meal plan for the evening is No milk (X1 = 0) 0. 499 pound of ground meat (X2) 0. 173 pound of chicken (X3) No fish (X4 = 0) No beans (X5 = 0) 0. 105 pound of spinach (X6) 0. 762 pound of white potatoes (X7) Each meal has a cost of $1. 75. The meal is fairly well -balanced (two meats, a green vegetable, and a potato). The weight of each item is realistic. This problem is very sensitive to changing food prices. Sensitivity analysis when prices change: Milk increases 10 cents/lb: no change in price or diet Milk decreases 10 cents/lb: no change in price or diet Milk decreases 30 cents/lb (to 30 cents): potatoes drop out and milk enters, price = $1. 42/meal Ground meat increases from $2. 35 to $2. 75: price = $1. 93 and spinach leaves the optimal solution Ground meat increases to $5. 25/lb: price = $2. 07 and meat leaves; milk, chicken, and potatoes in solution Fish decreases from $2. 25 to $2. 00/lb: no change Chicken increases to $3. 00/lb: price = $1. 91 and meat, fish, spinach, and potatoes in solution If meat and fish are omitted from the problem, the solution is chicken= 0. 774 lb milk= 1. 891 lb potatoes= 0. 33 lb If chicken and meat are omitted; fish= 0. 679 lb spinach= 0. 0988 lb milk= 2. 188 lb 8-13. a. Let X1= no. of units of internal modems produced per week X2= no. of units of external modems produced per week X3= no. of units of circuit boards produced per week X4= no. of units of floppy disk drives produced per week X5= no. of units of hard drives produced per week X6= no. of units of memory boards produced per week Objective function analysis: First find the time used on each test device: hours on test device 1 [pic] hours on test device 2 [pic] hours on test device 3 [pic] Thus, the objective function is aximize profit = (revenue) – (material cost) – )test cost) = (200X1 + 120X2 + 180X3 + 130X4 + 430X5 + 260X6 – 35X1 – 25X2 – 40X3 – 45X4 – 170X5 – 60X6)[pic] [pic] [pic] This can be rewritten as maximize profit =$161. 35X1 + 92. 95X2 + 135. 50X3 + 82. 50X4 + 249. 80X5 + 191. 75X6 subject to 7X1 + 3X2 + 12X3 + 6X4 + 18X5 + 17X6 lt; 120(60) Minutes on test device 1 2X1 + 5X2 + 3X3 + 2X4 + 15X5 + 17X6 lt; 120(60) Minutes on test device 2 5X1 + 1X2 + 3X3 + 2X4 + 9X5 + 2X6 lt; 100(60) Minutes on test device 3 All variables ( 0 b. The solution is X1= 496. 55 internal modems X2= 1,241. 38 external modems X3 through X6= 0 profit= $195,504. 80 c. The shadow prices, as explained in Chapter 7 and Module 7, for additional time on the three test devices are $21. 41, $5. 75, and $0, respectively, per minute. 8-14. a. Let Xi = no. of trained technicians available at start of month i Yi = no. of trainees beginning in month i Minimize total salaries paid = $2,000X1 + 2,000X2 + 2,000X3 + 2,000X4 + 2,000X5 + 900Y1 + 900Y2 + 900Y3 + 900Y4 + 900Y5 subject to 130X1 – 90Y1( 40,000 (Aug. need, hours) 130X2 – 90Y2( 45,000 (Sept. need) 130X3 – 90Y3( 35,000 (Oct. need) 130X4 – 90Y4( 50,000 (Nov. need) 130X5 – 90Y5( 45,000 (Dec. eed) X1= 350 (starting staff on Aug. 1) X2= X1 + Y1 – 0. 05X1 (staff on Sept. 1) X3= X2 + Y2 – 0. 05X2 (staff on Oct. 1) X4= X3 + Y3 – 0. 05X3 (staff on Nov. 1) X5= X4 + Y4 – 0. 05X4 (staff on Dec. 1) All Xi, Yi ( 0 b. The computer-generated results are: | |Trained | | | |Technicians |Trainees | |Month |Available |Beg inning | |Aug. 350 |13. 7 (actually 14) | |Sept. |346. 2 |0 | |Oct. |328. 8 |72. 2 (actually 72) | |Nov. |384. 6 |0 | |Dec. |365. 4 |0 | Total salaries paid over the five-month period = $3,627,279. 8-15. a. Let Xij = acres of crop i planted on parcel j wherei = 1 for wheat, 2 for alfalfa, 3 for barley = 1 to 5 for SE, N, NW, W, and SW parcels Irrigation limits: 1. 6X11 + 2. 9X21 + 3. 5X31( 3,200 acre-feet in SE 1. 6X12 + 2. 9X22 + 3. 5X32( 3,400 acre-feet in N 1. 6X13 + 2. 9X23 + 3. 5X33( 800 acre-feet in NW 1. 6X14 + 2. 9X24 + 3. 5X34( 500 acre-feet in W 1. 6X15 + 2. 9X25 + 3. 5X35( 600 acre-feet in SW [pic] water acre-feet total Sales limits: X11 + X12 + X13 + X14 + X15 ( 2,200 wheat in acres (= 110,000 bushels) X21 + X22 + X23 + X24 + X25 ( 1,200 alfalfa in acres (= 1,800 tons) X31 + X32 + X33 + X34 + X35 ( 1,000 barley in acres (= 2,200 tons) Acreage availability: X11 + X21 + X31( 2,000 acres in SE parcel X12 + X22 + X32( 2,300 acres in N parcel X13 + X23 + X33( 600 acres in NW parcel X14 + X24 + X34( 1,100 acres in W parcel X15 + X25 + X35( 500 acres in SW parcel Objective function: maximize profit [pic] b. The solution is to plant X12= 1,250 acres of wheat in N parcel X13= 500 acres of wheat in NW parcel X14= 312[pic] acres of wheat in W parcel X15= 137[pic] acres of wheat in SW parcel X25= 131 acres of alfalfa in SW parcel X31= 600 acres of barley in SE parcel X32= 400 acres of barley in N parcel Profit will be $337,862. 10. Multiple optimal solutions exist. c. Yes, need only 500 more water-feet. 8-16. Amalgamated’s blending problem will have eight variables and 11 constraints. The eight variables correspond to the eight materials available (three alloys, two irons, three carbides) that can be selected for the blend. Six of the constraints deal with maximum and minimum quality limits, one deals with the 2,000 pound total weight restriction, and four deal with the weight availability limits for alloy 2 (300 lb), carbide 1 (50 lb), carbide 2 (200 lb), and carbide 3 (100 lb). Let X1 through X8 represent pounds of alloy 1 through pounds of carbide 3 to be used in the blend. Minimize cost = 0. 12X1 + 0. 13X2 + 0. 15X3 + 0. 09X4 + 0. 07X5 + 0. 10X6 + 0. 12X7 + 0. 09X8 subject to manganese quality: 1  Ã‚  0. 70X1 + 0. 55X2 + 0. 12X3 + 0. 01X4 + 0. 05X5 ( 42 (2. 1% of 2,000) 2  Ã‚  0. 70X1 + 0. 55X2 + 0. 12X3 + 0. 01X4 + 0. 05X5 ( 46 (2. 3% of 2,000) silicon quality: 3  Ã‚  0. 15X1 + 0. 30X2 + 0. 26X3 + 0. 10X4 + 0. 025X5 + 0. 24X6 + 0. 25X7 + 0. 23X8 ( 86 (4. 3% of 2,000) 4  Ã‚  0. 15X1 + 0. 30X2 + 0. 26X3 + 0. 10X4 + 0. 025X5 + 0. 24X6 + 0. 25X7 + 0. 23X8 ( 92 (4. 6% of 2,000) carbon quality: 5  Ã‚  0. 03X1 + 0. 01X2 + 0. 03X4 + 0. 18X6 + 0. 20X7 + 0. 25X8 ( 101 (5. 5% of 2,000) 6  Ã‚  0. 03X1 + 0. 01X2 + 0. 03X4 + 0. 18X6 + 0. 20X7 + 0. 25X8 ( 107 (5. 35% of 2,000) Availability by weight: 7  Ã‚  X2 ( 300 8  Ã‚  X6 ( 50 9  Ã‚  X7 ( 200 10  Ã‚  X8 ( 100 One-ton weight: 11  Ã‚  X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 = 2,000 The solution is infeasible. 8-17. This problem refers to Problem 8-16’s infeasibility. Some investigative w ork is needed to track down the issues. The two issues are: 1. Requiring at least 5. 05% carbon is not possible. 2. Producing 1 ton from the materials is not possible. If constraints 5 and 11 are relaxed (or removed), one solution is X2 = 83. lb (alloy 2), X6 = 50 lb (carbide 1), X7 = 83. 6 lb (carbide 2), and X8 = 100 lb (carbide 3). Cost = $34. 91. Each student may take a different approach and other recommendations may result. 8-18. X1= number of medical patients X2= number of surgical patients Maximize revenue = $2,280X1 + $1,515X2 subject to 8X1 + 5X2( 32,850 (patient-days available = 365 days ( 90 new beds) 3. 1X1 + 2. 6X2 ( 15,000 (lab tests) 1X1 + 2X2( 7,000 (x-rays) X2( 2,800 (operations/surgeries) X1, X2( 0 Problem 8-18 solved by computer: X1= 2,791 medical patients X2= 2,105 surgical patients revenue= $9,551,659 per year To convert X1 and X2 to number of medical versus surgical beds, find the total number of hospital days for each type of patient: medical= (2,791 patients)(8 days/patient) = 22,328 days surgical= (2,105 patients)(5 days/patient) = 10,525 days total= 32,853 days This represents 68% medical days and 32% surgical days, which yields 61 medical beds and 29 surgical beds. (Note that an alternative approach would be to formulate with X1, X2 as number of beds. ) See the printout on the next page for the solution and sensitivity analysis. 8-19. This problem, suggested by Professor C. Vertullo, is an excellent exercise in report writing. Here is a chance for students to present management science results in a management format. Basically, the following issues need to be addressed in any report: (a)  Ã‚  As seen in Problem 8-18, there should be 61 medical and 29 surgical beds, yielding $9,551,659 per year. (b)  Ã‚  Referring to the QM for Windows printout, there are no empty beds because the slack for constrain 1 has a value of 0.. (c)  Ã‚  There are 876 (the slack for constraint 2) lab tests of unused capacity. (d)  Ã‚  The x-ray is used to its maximum (slack for constraint 3 is 0) and has a $65. 5 dual price. The revenue would increase by this amount for each additional x-ray. (e)  Ã‚  The operating room still has 695 operations available (the slack for constraint 4). [pic] [pic] 8-20. For the Low Knock Oil Company example it was originally assumed that a one to one ratio of raw materials (crude oil) to finished goods (gasoline). In reality, that ratio is closer to 46%. Hence, the example problem needs to be modified with 0. 46 as the coefficient throughout the first two constraints as follows: Minimize 30X1 + 30X2 + 34. 80X3 + 34. 80X4 subject to: 0. 46X1 + 0. 46X3( 25000 0. 46X2+ 0. 46X4( 32000 0. 10 X1 + 0. 15X3 ( 0 0. 05X2 – 0. 25X4 ( 0 The rounded solution is X1 = 32609; X2 = 57971; X3 = 21739; X4 = 11594; Cost = 3877391 8-21. Minimize time = 12XA1 + 11XA2 + 8XA3 + 9XA4 + 6XA5 + 6XA6 + 6XG1 + 12XG2 + 7XG3 + 7XG4 + 5XG5 + 8XG6 + 8XS1 + 9XS2 + 6XS3 + 6XS4 + 7XS5 + 9XS6 subject to XA1+ XA2+ XA3+ XA4+ XA5+ XA6= 200 XG1+ XG2+ XG3+ XG4 + XG5+ XG6= 225 XS1+ XS2+ XS3+ XS4+ XS5+ XS6= 275 XA1+ XG1+ XS1= 80 XA2+ XG2+ XS2= 120 XA3+ XG3+ XS3= 150 XA4+ XG4+ XS4= 210 XA5+ XG5+ XS5= 60 XA6+ XG6+ XS6= 80 All variables ( 0 Solution: |Source |Destination |Number of |(Station) |(Wing) |Trays | |5A |5 |60 | |5A |6 |80 | |5A |3 |60 | |3G |1 |80 | |3G |3 |90 | |3G |4 |55 | |1S |4 |155 | |1S |2 |120 | Optimal cost = 4,825 minutes. Multiple op timal solutions exist. 8-22. Let Xi = proportion of investment invested in stock i for i = 1, 2, . . . , 5 Minimize beta = 1. 2X1 + 0. 85X2 + 0. 55X3 + 1. 40X4 + 1. 25X5 subject to X1 + X2 + X3 + X4 + X5 = 1total of the proportions must add to 1 0. 11X1 + 0. 09X2 + 0. 065X3 + 0. 15X4 + 0. 13X5 ( 0. 11return should be at least 11% X1 ( 0. 5no more than 35% in any single stock X2 ( 0. 35 X3 ( 0. 35 X4 ( 0. 35 X5 ( 0. 35 Xi ( 0 for i = 1, 2, . . . , 5 b. Solving this on the computer, we have X1 = 0 X2 = 0. 10625 X3 = 0. 35 X4 = 0. 35 X5 = 0. 19375 Minimum beta = 1. 015 Return = 0. 11(0) + 0. 09(0. 10625) + 0. 065(0. 35) + 0. 15(0. 35) + 0. 13(0. 19375) = 0. 11 8-23. Let A = 1,000 gallons of fuel to purchase in Atlanta L = 1,000 gallons of fuel to purchase in Los Angeles H = 1,000 gallons of fuel to purchase in Houston N = 1,000 gallons of fuel to purchase in New Orleans FA = fuel remaining when plane lands in Atlanta FL = fuel remaining when plane lands in Los Angeles FH = fuel remaini ng when plane lands in Houston FN = fuel remaining when plane lands in New Orleans Minimize cost = 4. 15A + 4. 25L + 4. 10H + 4. 18N subject to A + FA ( 24minimum amount of fuel on board when leaving Atlanta A + FA ( 36maximum amount of fuel on board when leaving Atlanta L + FL ( 15minimum amount of fuel on board when leaving Los Angeles L + FL ( 23maximum amount of fuel on board when leaving Los Angeles H + FH ( 9minimum amount of fuel on board when leaving Houston H + FH ( 17maximum amount of fuel on board when leaving Houston N + FN ( 11minimum amount of fuel on board when leaving New Orleans N + FN ( 20maximum amount of fuel on board when leaving New Orleans FL = A + FA – (12 + 0. 05(A + FA – 24)) This says that the fuel on board when the plane lands in Los Angeles will equal the amount on board at take-off minus the fuel consumed on that flight. The fuel consumed is 12 (thousand gallons) plus 5% of the excess above 24 (thousand gallons). This simplifies to: 0. 95A + 0. 95 FA – FL = 10. 8 Similarly, FH = L + FL – (7 + 0. 05(L + FL – 15)) becomes 0. 95L + 0. 95FL – FH = 6. 25 FN = H + FH – (3 + 0. 05(H + FH – 9)) becomes 0. 95H + 0. 95FH – FN = 2. 55 FA = N + FN – (5 + 0. 05(N + FN – 11)) becomes 0. 95N + 0. 95FN – FA = 4. 45 All variables ( 0 The optimal solution is A=18 (1,000 gallons of fuel to purchase in Atlanta) FA=6 (1,000 gallons of fuel remaining when plane lands in Atlanta) L=3 (1,000 gallons of fuel to purchase in Los Angeles) FL=12 (1,000 gallons of fuel remaining when plane lands in Los Angeles) H=1 (1,000 gallons of fuel to purchase in Houston) FH=8 (1,000 gallons of fuel remaining when plane lands in Houston) N=5 (1,000 gallons of fuel to purchase in New Orleans) FN=6 (1,000 gallons of fuel remaining when plane lands in New Orleans) Total cost = 112. 45 (( 1,000) Solutions to Internet Homework Problems 8-24. Let X1 = number of Chaunceys mixed X2= number of Sweet Italians mixed X3= number of bourbon on the rocks mixed X4= number of Russian martinis mixed Maximize total drinks = X1 + X2 + X3 + X4 subject to 1X1 +4X3 ( 52 oz (bourbon limit) 1X1 +1X2 ( 38 oz (brandy limit) 1X1 +2[pic]X4 ( 64 oz (vodka limit) X2 +1[pic]X4 ( 24 oz (dry vermouth limit) 1X1 +2X2 ( 36 oz (sweet vermouth limit) All variables ( 0 Because a Chauncey (X1) is [pic] sweet vermouth, it requires 1 oz of that resource (each drink totals 4 oz). Problem 8-27 solved by computer: Mix 25. 99 (or 26) Chaunceys (X1) Mix   5. 00 (or 5) Sweet Italians (X2) Mix   6. 50 (or 6[pic]) bourbon on the rocks (X3) Mix 14. 25 (or 14[pic]) Russian martinis (X4) This is a total of 51. 75 drinks (in five iterations). 8-25. Minimize 6X11 + 8X12 + 10X13 + 7X21 + 11X22 + 11X23 + 4X31 + 5X32 + 12X33 subject to X11 + X12 + X13( 150 X21 + X22 + X23( 175 X31 + X32 + X33( 275 X11 + X21 + X31= 200 X12 + X22 + X32= 100 X13 + X23 + X33= 300 All variables ( 0 The solution is: X11 = 25, X13 = 125, X23 = 175, X31 = 175, X32 = 100 Cost = $4,525. 8-26. Let Xi = number of BR54 produced in month i, for i = 1, 2, 3. Yi   = number of BR49 produced in month i, for i = 1, 2, 3. IXi = number of BR54 units in inventory at end of month i, for i = 0, 1, 2, 3. IYi = number of BR49 units in inventory at end of month i, for i = 0, 1, 2, 3. Minimize cost = 80(X1 + X2 + X3) + 95(Y1 + Y2 + Y3) + 0. 8(IX1 + IX2 + IX3) + 0. 95(IY1 + IY2 + IY3) Subject to: IX0 = 50initial inventory of BR54 IY0 = 50initial inventory of BR49 IX3 = 100ending inventory of BR54 IY3 = 150ending inventory of BR49 X1 + Y1 ( 1,100maximum production level in August X2 + Y2 ( 1,100maximum production level in September X3 + Y3 ( 1,100maximum production level in October X1 + IX0 = 320 + IX1  Ã‚  BR54 requirements for August X2 + IX1 = 740 + IX2  Ã‚  BR54 requirements for September X3 + IX2 = 500 + IX3  Ã‚  BR54 requirements for October Y1 + IY0 = 450 + IY1  Ã‚  BR49 requirements for August Y2 + IY1 = 420 + IY2  Ã‚  BR49 requirements for September Y3 + IY2 = 480 + IY3  Ã‚  BR49 requirements for October All variables ( 0 A computer solution to this results in IX0 = 50, IX1 = 190, IX2 = 130, IX3 = 100, IY0 = 50, IY3 = 150, X1 = 460, X2 = 680, X3 = 470, Y1 = 400, Y2 = 420, Y3 = 630. All other variables = 0. The total cost = $267,028. 50. Solution to Chase Manhattan Bank Case This very advanced and challenging scheduling problem can be solved most expeditiously using linear programming, preferably integer programming. Let F denote the number of full-time employees. Some number, F1, of them will work 1 hour of overtime between 5 p. m. and 6 p. m. each day and some number, F2, of the full-time employees will work overtime between 6 p. m. and 7 p. m. There will be seven sets of part-time employees; Pj will be the number of part-time employees who begin their workday at hour j, j = 1, 2, . . . , 7, with P1 being the number of workers beginning at 9 a. m. , P2 at 10 a. . , . . . , P7 at 3 p. m. Note that because part-time employees must work a minimum of 4 hours, none can start after 3 p. m. since the entire operation ends at 7 p. m. Similarly, some number of part-time employees, Qj, leave at the end of hour j, j = 4, 5, . . . , 9. The workforce requirements for the first two hours, 9 a. m. a nd 10 a. m. , are: F + P1( 14 F + P1 + P2 ( 25 At 11 a. m. half of the full-time employees go to lunch; the remaining half go at noon. For those hours: 0. 5F + P1 + P2 + P3( 26 0. 5F + P1 + P2 + P3 + P4 ( 38 Starting at 1 p. m. , some of the part-time employees begin to leave. For the remainder of the straight-time day: F + P1 + P2 + P3 + P4 + P5 – Q4( 55 F + P1 + P2 + P3 + P4 F + P1 + P2 + P5 + P6 – Q4 – Q5( 60 F + P1 + P2 + P3 + P4 + P5 F + P1 + P6 + P7 – Q4 – Q5 – Q6( 51 F + P1 + P2 + P3 + P4 + P5 + P6 F + P1 + P7 – Q4 – Q5 – Q6 – Q7( 29 For the two overtime hours: F1 + P1 + P2 + P3 + P4 + P5 + P6 F1 + P1 + P2 + P7 – Q4 – Q5 – Q6 – Q7 – Q8( 14 F2 + P1 + P2 + P3 + P4 + P5 + P6 + P7 F1 + P1 + P2 – Q4 – Q5 – Q6 – Q7 – Q8 – Q9( 9 If the left-hand sides of these 10 constraints are added, one finds that 7F hours of full-time labor are used in straight time (although 8F are paid for), F1 + F2 full-time labor hours are used and paid for at overtime rates, and the total number of part-time hours is 0P1 + 9P2 + 8P3 + 7P4 + 6P5 + 5P6 + 4P7 – 6Q4– 5Q5 – 4Q6 – 3Q7 – 2Q8 – Q9 ( 128. 4 which is 40% of the day’s total r equirement of 321 person-hours. This also leads to the objective function. The total daily labor cost which must be minimized is Z = 8(10. 11)F + 8. 08(F1 + F2) + 7. 82(10P1 + 9P2 + 8P3 + 7P4 + 6P5 + 5P6 + 4P7 – 6Q4 – 5Q5 – 4Q6 – 3Q7 – 2Q8 – Q9) Total overtime for a full-time employee is restricted to 5 hours or less, an average of 1 hour or less per day per employee. Thus the number of overtime hours worked per day cannot exceed the number of full-time employees: F1 + F2 ( F Since part-time employees must work at least 4 hours per day, Q4 ( P1 for those leaving at the end of the fourth hour. At the end of the fifth hour, those leaving must be drawn from the P1 – Q4 remaining plus the P2 that arrived at the start of the second hour: Q5 ( P1 + P2 – Q4 Similarly, for the remainder of the day, Q6( P1 + P2 + P3 – Q4 – Q5 Q7( P1 + P2 + P3 + P4 – Q4 – Q5 – Q6 Q8( P1 + P2 + P3 + P4 + P5 – Q4 – Q5 – Q6 – Q7 Q9( P1 + P2 + P3 + P4 + P5 + P6 – Q4 – Q5 – Q6 – Q7 – Q8 To ensure that all part-timers who began at 9 a. m. do not work more than 7 hours: Q4 + Q5 + Q6 + Q7 ( P1 Similarly, Q4 + Q5 + Q6+ Q7 + Q8 ( P1 + P2 Q4 + Q5 + Q+ Q7 + Q8 + Q9 ( P1 + P2 + P3 Finally, to ensure that all part-time employees leave at some time: P1 + P2 + P3 + P4 + P5 + P6 + P7 = Q4 + Q5 + Q6 + Q7 + Q8 + Q9 The resulting problem has 16 integer variables and 22 constraints. If integer programming software is not available, the linear programming problem can be solved and the solution rounded, making certain that none of the constraints have been violated. Note that the integer programming solution might also need to be adjusted- if F is an odd integer, 0. 5F will not be an integer and the requirement that â€Å"half† of the full-time employees go to lunch at 11 a. m. and the other half at noon will have to be altered by assigning the extra employee to the appropriate hour. 1. The least-cost solution requires 29 full-time employees, 9 of whom work two hours of overtime per day. In actuality, 18 of the full-time employees would work overtime on two different days and 9 would work overtime on one day. Fourteen of the full-time workers would take lunch at 11 a. m. and the other 15 would take it at noon. Eleven part-timers would begin at 11 a. m. , with 9 of them leaving at 3 p. m. and the other 2 at 4 p. m. Fifteen part-time employees would work from noon until 4 p. m. , and 5 would work from 2 p. m. until 6 p. m. The resulting cost of 232 hours of straight time, 18 hours of overtime, and 126 hours of part-time work is $3,476. 28 per day. This solution is not unique- other work assignments can be found that result in this same cost. 2. The same staffing would be used every day. In fact, one would expect different patterns to present themselves on different days; for example, Fridays are usually much busier bank days than the others. In addition, the person-hours required for each hour of the day are assumed to be deterministic. In a real situation, wide fluctuations will be experienced in a stochastic manner. The optimal solution results in a considerable amount of idle time, partly caused by the restriction that employees can start at the beginning of an hour and leave at the end. Eliminating this restriction might yield better results at the risk of increasing the problem size.

Pathways to entry into the practice of professional nursing is Essay

Pathways to entry into the practice of professional nursing is confusing - Essay Example I strongly believe that these numerous entry points are not confusing, but they offer a range of benefits to nursing candidates. When there are many entry points to the practice of professional nursing, candidates get a great exposure to several potential entry choices. The numerous entry points greatly assist students to choose the most appropriate one by giving specific focus to their long term career goals, opportunities for college entrance, and personal and work obligations. These options are also beneficial for candidates to choose the most affordable entry point and avoid excess financial burden. To illustrate, as Black (2013, p. 134) purports, typically the annual cost of diploma and associate degree programs is less than baccalaureate degree programs. Those candidates who choose to attend local schools and live at home may incur lesser costs than students attending schools at distance and living in hostels. Hence, they can thoughtfully identify the entry point that would best fit to their financial interests. Another potential benefit is that students can take the issues of accreditation and articula tion into account while considering entry choice. Similarly, the emerging entry points address various issues associated with traditional entry points, and therefore students can avoid unnecessary concerns associated with their entry into the nursing profession. To sum up, the numerous entry points do not cause any confusion to students who have a clear vision of their long term career goals and financial potentials. Maneval, R. E & Teeter, M. M. (2010). THE STUDENT PERSPECTIVE on RN-Plus-10 Legislation: A Survey of Associate Degree and Diploma Nursing Program Students. Nursing Education Perspectives 31 (6): 358-361. Raines, F & Taglaireni, M. E. (2008). Career Pathways in Nursing: Entry Points and Academic Progression. The Online Journal of Issues in Nursing. Retrieved from