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Role Of Mathematical Programming

Introduction In order to survive and lead today’s highly competitive and demand driven market, there is a great deal of pressure on management to make economical decisions. One of the essential managerial skills is the ability to allocate and utilize resources appropriately in the efforts of achieving the optimal performance efficiently. Mathematical models have long played an important role in management and economics but it is only in the last few decades that management per se has received the sort of rigorous study that permits the application of mathematics. It is one of the primary tools used by operations researchers in making decisions. Mathematical programming Mathematical programming is the OR technique that has been most widely applied in management and economics. It has been used to solve a considerable range of problems in financial markets – forming portfolios of equities, bonds, loans and currencies, generalized hedging, capital budgeting, cash management, insurance management, equity and bond index tracking, estimating the implied risk neutral probabilities for options, designing leveraged leases, computing the maximum loss sustained by shareholders, spotting insolvent banks, sorting out the failure of a stock exchange and understanding the forces leading to financial innovations. It deals with models comprising of an objective function and a set of constraints. An objective function is a mathematical expression of the quantity to be maximized or minimized. For example, manufacturers may wish to maximize production or minimize costs, advertisers may wish to maximize a product’s exposure, and financial analysts may wish to maximize rate of return. Constraints are mathematical expressions of restrictions that are placed on potential values of the objective function. For example, production may be constrained by the total amount of labor at hand and machine production capacity, an advertiser may be constrained by an advertising budget, and an investment portfolio may be restricted by the allowable risk. Symbolically, mathematical models in operations research may be viewed generally as determining the values of the decision variables which will Optimize subject to The function is the objective function while represents the constraint, whereis constant. The constraintsare the non-negativity constraints. In general,optimization of the objective function signifies either amaximization or minimizationof this function. The types of the objective and constraint functions of a mathematical model depend directly on the systems which they represent. Thus, these functions may be linear or non-linear. Also the decision variables may be continuous or discrete and the parameters of the system may be deterministic or probabilistic. The result of this diversity in system representation is the development of a corresponding number of optimization techniques suitable for solving these models. These mainly include linear programming, integer programming, goal programming, non-linear programming, dynamic programming, and stochastic programming. The Mathematical Programming Approach There is an orderly sequence of steps that is followed for a systematic formulation, solution and implementation of a mathematical programming model. These steps could be applied to the development of any management science model. Although the practical applications of mathematical programming cover a broad range of problems, it is possible to distinguish five general stages that the solution of any mathematical programming should follow. These stages along with their main characteristics are as follows : A. Formulating the Model The first step to be taken in a practical application is the development of the model. The following are the elements that define the model structure : Selection of a time horizon Selection of decision variables and parameters Definition of constraints Selection of the objective function B. Gathering the Data After defining the model, the data required to define the parameters of the model must be collected. This involves the data regarding the objective function coefficients, the constraint coefficients and the right hand side of the constraints. C. Obtaining an Optimal Solution Due to the lengthy nature of calculations required to obtain the optimal solution of a mathematical programming model, a digital computer is invariably used in this stage of model implementation. Nowadays, all the computer manufacturers offer highly efficient codes to solve mathematical programming models. D. Applying Sensitivity Analysis Sensitivity analysis, also called post-optimum analysis, is performed on the optimal solutions obtained for the linear programming problems originally formulated. This analysis is important for several reasons : Data uncertainity Dynamic considerations Input errors E. Testing and Implementing the Solution Once the optimal solution is obtained, it should be tested fully to ensure that the model clearly represents the real situation. The importance of conducting sensitivity analysis as part of this testing effort has already been discussed. If the solution is unacceptable, new refinements have to be incorporated in the model and new solutions obtained until the mathematical programming model is adequate. When the testing is over, the model can be implemented. Implementation usually means solving the model with real data to reach a decision or a set of decisions. Types of Mathematical Programming A. Linear programming Linear programming is one of the most successful disciplines within the field of Operational Research. It arose as a mathematical model developed during the second world war to plan expenditures and returns in order to reduce costs to the army and increase losses to the enemy. It was kept secret until 1947. Post war, many industries found its use in their daily planning. Linear programming is a technique for making decisions under certainity i.e.; when all the courses of options available to an organization are known in advance and the objective of the firm along with its constraints are quantified. Out of all the possible alternative that course of action is chosen that which yields the optimal results. Mathematically, linear programming problem calls for finding non-negativeso as to maximize a linear functionsubject to a system of linear equations : There are two extensions of Linear programming which are as follows : a) Integer Linear programming The Integer Linear Programming (ILP) is an extension of Linear programming where all of the variables must only take on integer values. b) Mixed Integer Linear Programming The Mixed integer Linear Programming (MILP) is also an extension of the Linear programming, but some of the variables must take on integer values while others take on real values. B. Quadratic programming Quadratic Programming is a special type of mathematical optimization problem. It is the problem of optimizing (minimizing or maximizing) a quadratic function of several variables subject to linear constraints on these variables. C. Goal Prgramming Goal Programming is promulgated as an aid for decision-making problems with multiple, possibly conflicting goals. In a typical goal programming model, each goal is formulated as a constraint. There are two variables associated with each goal (each constraint), over-achievement deviation and under-achievement deviation. The value of these two deviational variables measure how well the corresponding goal is accomplished. An objective function in a goal programming formulation is usually a linear function in deviational variables. Specifically, the objective function takes the weighted summation of the deviational variables. The weights assigned to a deviational variable indicate the importance of the corresponding goal in decision-making process. The objective is thus to minimize the weighted sum of deviations from goal achievement, i.e., to accomplish the best overall achievement. D. Dynamic Programming Dynamic Programming is a mathematical programming technique which fragments a large problem into several smaller problems. The approach is to solve the all the smaller, easier problems individually in order to reach a solution to the original problem. This technique is useful for making decisions that consist of several steps, each of which also requires a decision. In addition, it is assumed that the smaller problems are not independent of one another given they contribute to the larger question. E. Stochastic Programming Many optimization problems are described by uncertain parameters. When these uncertain parameters can be considered as random variables and have known probability distributions, new optimization problems can be formulated that involve expected values of these random variables. In this manner, a new problem (called the deterministic equivalent) is obtained that removes the uncertainty and results in a deterministic optimization problem. This is the approach of Stochastic Programming. Application areas of Mathematical Modeling The applications of mathematical modeling in management and economics today are so manifold that it is difficult to list them down. A few of the major application areas of mathematical models are as follows :

UOP Learning Environment for Grade One Pupil & Classroom Activities Discussion

UOP Learning Environment for Grade One Pupil & Classroom Activities Discussion.

Assignment ContentSchedules, transitions, and routines will vary in learning environments based on age and developmental level. Schedules should be used as guides rather than requirements to allow for unexpected learning opportunities. In early childhood settings, transitions occur frequently and sometimes account for 25% of the child’s day. Routines are also important for early learners, because they provide predictability, stability, and security for children.Choose an early education age/grade level (preschool–Grade 3) and create a schedule that:Includes times, activities, transitions, and routinesFactors in your classroom-management philosophyReview Ch. 3, “Sample Daily Schedules,” of Creating Environments for Learning: Birth to Age Eight located in this week’s Learning Activities folder for ideas or guidance. Please note: You may not copy these schedules for this assignment.Write a minimum 350-word analysis that addresses the following questions:Why are schedules, transitions, and routines critical to your success in the classroom?How will these activities, transitions, and routines promote student engagement?Why is it important to have schedules and routines in place at the beginning of the school year?How might you adapt the schedule you created to accommodate children with diverse needs (i.e., learners who are gifted, learners who have special needs, English language learners, etc.)?What impact does preparation and instructional planning have on whether or not students follow these routines and procedures?Using “Figure 3.3: Environmental Assessment: Schedules, Transitions, and Routines” of Creating Environments for Learning: Birth to Age Eight to assess your schedule, which items have you accomplished in your schedule?Cite references to support your assignment.Format your citations and analysis according to APA guidelines.Submit your schedule and analysis.ResourcesCenter for Writing ExcellenceReference and Citation GeneratorGrammar and Writing Guides
UOP Learning Environment for Grade One Pupil & Classroom Activities Discussion

MGT 232 Saudi Electronic University Teamwork and Proper Communication Discussion

essay helper free MGT 232 Saudi Electronic University Teamwork and Proper Communication Discussion.

ons – PLEASE READ THEM CAREFULLY The Assignment must be submitted on Blackboard (WORD format only) via allocated folder.Assignments submitted through email will not be accepted.Students are advised to make their work clear and well presented, marks may be reduced for poor presentation. This includes filling your information on the cover page.Students must mention question number clearly in their answer.Late submission will NOT be accepted.Avoid plagiarism, the work should be in your own words, copying from students or other resources without proper referencing will result in ZERO marks. No exceptions. Assignment requires references.All answered must be typed using Times New Roman (size 12, double-spaced) font. No pictures containing text will be accepted and will be considered plagiarism).Submissions without this cover page will NOT be accepted.
MGT 232 Saudi Electronic University Teamwork and Proper Communication Discussion

Art Museum Visit Reflection Paper

Art Museum Visit Reflection Paper. Visit to the Metropolitan Museum of Art at New York City Last week I visited the Metropolitan Museum of Art at New York City. This museum, also known as The Met is a huge building with nineteen departments and around two billion art pieces stored and displayed in its art galleries. The main art gallery of the museum, i.e. The Met is one of the largest galleries of the world There are several categories of art works displayed in different portions of the museum. The main categories and collections of the art works displayed at the museum are American art, Ancient Near Eastern art, American decorative arts, Asian art, Egyptian art, Greek and Roman art, African art, South American art, art related to arms and armory, European art, Islamic art and religious collections. The art works include various forms, though paintings and sculpture are the main forms. Collections comprising weapons and armory, musical instruments, costumes and building interiors are some other important art forms at display in the museum. Visit to museums has always been a pleasant experience for me. Museums open doors to a world of fantasy. By entering the doors of a good museum, it is possible to close off the doors of mind to the harsh realities of the real world for a while. Visit to a museum is akin to visiting a fairy land. It is a wonderful and refreshing experience to see the relics of past from such close proximity. I have particularly been interested in paintings. A painting is nothing less than an incarnation of the imagination of the painter. The manner in which an artist brings the lifeless canvas to life by using strokes of his or her brush is amazing. It is a life created by the artist using nothing more than few mundane objects like a brush, colors, oil or water and a canvas. Religious art works have always intrigued me a lot due to my interest in comparative study of religions and the collection at the Met was a treat for my eyes. I had a chance to observe many beautiful and mesmerizing artworks at the museum but at the moment I will discuss the following three artworks, since the memories of these artworks are still fresh in my mind due to the strong impact made by them: Madonna and Child Enthroned with Saints Stoclet Madonna Temple of Dendur Madonna and Child Enthroned with Saints were done by Italian painter named Raphael. Raphael belonged to the High Renaissance era of art. This form of art was patronized by Pope Julius II and Italy was the focal point of this era and Michelangelo, Leonardo de Vinci and Raphael were the prominent artists This is a conservative piece of art and it was painted by Raphael when he was about twenty one years old. This painting as the name depicts, shows Saint John, Saint Peter and Saint Paul with Madonna and the child. Raphael had painted this work for the convent of Sant’Antonio which was held at Perugia. On the desires of the nuns, Raphael painted this work in a very conservative manner and the painted shows Saint John and the Christ fully clothes in this work. Considering that it was an early work, this work has a strong influence of Raphael’s teacher Perugino. A significant feature of this piece of art is the fact that there is only one panel of any altarpiece created by Raphael in the United States and apart from this work there is no other similar artwork by Raphael in any American museum.. This art piece was completed in year 1504 and oil and gold have been used as medium on a wooden base. The second piece of art is also about Madonna and child Christ. It is a painting as well. This piece shares another commonality with Raphael’s piece in terms that it has also been painted by an Italian artist. This piece was painted by Duccio di Buoninsegna in the medieval era. The medium used by Duccio for this painting is tempera and gold on a base of wood. This painting was bought by the Metropolitan Museum of Art for a cost of around forty five million US dollars and it is reportedly the costliest purchase of this museum. Surviving works of Duccio are very rare and this is the reason for the high value of this painting. This painting is known as Stoclet Madonna due to the fact that the name of the family which privately owned this paiting before its acquisition by the museum was Stoclet. The year of completion of this painting is around 1300 A.D and portrays the child Christ and the Virgin Mary only. Significant feature noted in this painting was the simplistic portrayal of the child and the mother and use of rounded forms. The third artwork which I want to write about in this narrative is not a painting but a temple. This temple was gifted by the government of the Republic of Egypt to United States in 1978. The original location of this temple was around Aswan dam on the river Nile. This temple was endangered by submersion due to construction of the dam and hence it was dismantled from its original location to save. In the 15th century BC, Egypt was ruled by a Roman governor named Petronius. This temple was built by Petronius in dedication to ancient Egyptian goddess Isis and her brother Osiris. Emperor Augustus of Rome commissioned this temple. The structure of the temple is made of sandstone and the temple has various engravings and carvings depicting the religious symbols of the Roman-Egyptian era of the 15th century BC. Base of the temple shows carvings of lotus plants and papyrus. These symbols are associated with river Nile and river Nile in turn was religiously a symbol of life for the ancient Egypt in a similar manner as river Ganga is a religious connotations for Hindus in India. The most prominent theme that is repeated in the temple is the carvings of the forms of goddess Isis, her brother Osiris and their son Horus. Another striking feature is graffiti scribbled in English that were left by the visitors when the temple was in its original location. Art Museum Visit Reflection Paper

NR 439 Chamberlain College of Nursing Clarifying Research Worksheet

NR 439 Chamberlain College of Nursing Clarifying Research Worksheet.

Discussion QuestionsAccess the following information. You may read the PDF online or download it.American Nurses Association. (2014). Fast facts: The nursing workforce 2014: Growth, salaries, education, demographics & trends. ANA. Retrieved from https://www.nursingworld.org/globalassets/practiceandpolicy/workforce/fastfacts_nsgjobgrowth-salaries_updated8-25-15.pdf (Links to an external site.)Review the data presented in the ANA Fast Facts and describe some of the key attributes/characteristics of this sample of the nursing workforce.Discuss some of the data that you found interesting; include what you believe the purpose (intent) of ANA sharing these results.The instruments and tools that we use to collect data need to be reliable and valid. Define these terms and explain the importance of each. Share one way that can be used to collect data that you were not aware of or familiar with.HOMEWORK 2PurposeA baccalaureate nurse understands, relates, and values the fundamental elements of research, process, and designs as a foundation for an evidence-based practice (American Association of Colleges of Nurses, 2008; Quality and Safety Education for Nurses, 2018). This assignment provides a learning activity to demonstrate understanding of the significance of research, the types of research and designs, the importance of sampling, utilization, and how research contributes to a credible nursing profession.Course OutcomesThis assignment enables the student to meet the following Course Outcomes.CO 1: Examine the sources of evidence that contribute to professional nursing practice. (PO 7)CO 2: Apply research principles to the interpretation of the content of published research studies. (PO 4 & 8)CO 5: Recognize the role of research findings in evidence-based practice. (PO 7 & 8)Due DateSubmit the completed this assignment by Sunday, 11:59 p.m. MT at the end of Week 5.PointsThis assignment is worth 225 points.Directions for Preparing the Scholarly WorksheetRead each of the instructions.Download and complete the required Clarifying Research Worksheet under Templates below.Review the Week 5 Assignment Tutorial (Links to an external site.) (Transcript (Links to an external site.)) which reviews your Week 5 Assignment. Tutorial may look slightly different session to session. Grading criteria and rubric will be the same.Two or more supporting scholarly sources are required. Textbooks are not allowed and should not be used as a scholarly source. Use the Chamberlain Library to locate relevant, scholarly sources.No more than two direct quotes are allowed. You should be using mostly your own words to demonstrate your understanding of the topics/criteria for this assignment. Citations and references must be included.Submit the completed assignment on the Week 5: Assignment.TemplatesClarifying Research Worksheet (Links to an external site.)Best PracticesFor questions about this assignment, please contact your instructor.Spell check for spelling and grammar errors prior to final submission. Please see the grading criteria and rubrics.Please use your browser’s File setting to save or print this page.Integrity Matters: Review the syllabus and follow the Academic Integrity policy in the Student Handbook (Links to an external site.)Scholarly Sources and Citations Two or more supporting scholarly sources are required.No more than two direct quotes are allowed.Use APA format in citations and references.ReferencesAmerican Association of Colleges of Nurses (AACN). (2008). Executive summary: The essentials of baccalaureate education for professional nursing practice. http://www.aacnnursing.org/Education-Resources/AAC…Quality and Safety Education for Nurses (QSEN). (2018). QSEN knowledge, skills, and attitude competencies. http://qsen.org/competencies/pre-licensure-ksas/
NR 439 Chamberlain College of Nursing Clarifying Research Worksheet