Project Management Case Study Example | Topics and Well Written Essays - 750 words

Project Management - Case Study Example This is an added advantage for Rachel since at that time there is no distractions hence total concentration. However, although she gets to work early, in the first twenty minutes after getting into the office, she does nothing constructive. Instead, she takes these twenty minutes to socialize with her colleague Neil. Although socializing gets an individual in a good mood to start off the day, it is unadvisable since it may also act as a distraction (Erik and Clifford, 2011). Question 2: What does the case tell you about what it is like to be a project manager? It is worth noting that project management is not an easy task since it is a leadership position. Therefore, as a project manager, Rachel should arrive early in order to set a trend for her team members on punctuality and time management. More so, by the time the company managing director arrives, Rachel should be able update him or her on the progress of the project, as well as, the working team. There are a number of manageri al traits that are required of a project manager. First, project manager is a supervisor that over sees all the operations concerning the project (Erik and Clifford, 2011). For instance, Rachel spends most of the day moving from one office to the other supervising her team, consulting with her workmates as well as reporting to her boss. Secondly, as a project manager, one should play an assistive role to his or her colleagues. For example, Rachel helps another IS project manager in reviewing the project and bringing it back on track. Finally, a project manager should be social and keep in touch with everyone within and outside their organization. Rachel communicates with her team members and discusses extensively with her counterparts from client firms. These, among other reasons, show that the role of a project manager is a generally a one man task. 2) Moss and McAdams Accounting firm This case study is based on an occurrence at the Moss and McAdams (M&M) firm that caused a conflic t of interest between two managers: Bruce Palmer and Ken Crosby. The disagreement was on whom Mr. Zeke Olds, a very resourceful person, should work for. However, there are a number of reasons that place Crosby as the most suitable person to work with Olds. Question 1: If you were Palmer at the end of the case, how would you respond? The first reason would be that it is not advisable to have a member of the team who is not fully committed to the roles he or she is supposed to play. In addition, it would be best for Bruce to avoid conflicting with Crosby who was an important colleague (Erik and Clifford, 2011). Question 2: What, if anything, could Palmer have done to avoid losing Olds? According to Erik and Clifford, 2011, Although Palmer would have taken some impromptu actions to avoid losing Olds; it was the best action at the time. Initially, he could have held a discussion with both Crosby and Olds for the purpose of making a proper timetable as well as setting rules that would no t disadvantage either party. The second reason was that Palmer took quite a while before communicating with Ruby Sands, the manager in charge of assigning personnel to various accounts at the Green Bay Office in which Palmer and Cosby were based. Had he communicated his wish earlier, the situation would have been kept in control and his project, the Johnsonville Project, would have been kept on schedule. However, Crosby was not an understanding colleague since he expected favors although he could not return

Sustainable Management Futures Essay Example | Topics and Well Written Essays - 750 words - 2

Sustainable Management Futures - Essay Example The employer should have justifiable evidence that can convince an outside observer of her claims. The employee should also be convicted that this action of making public the wrongdoings will lead to changes being done. The Disclosure Act 1998 requires employees not to engage in whistle blowing activities. Loyalty is having unwavering allegiance to an affiliation or person Integrity on the other hand is being free of any form of dishonest behavior (Johnson, 2003: 279). When whistle blowing the employee who is loyal to the organization should seek the best for that organization and make justifiable accusations that are not aimed at achieving selfish gain but helping the general majority. Whistle blowing for the right reasons is a positive force in the society as it ensures that people maintain accountability and ethics. Lying is not justifiable at any one time. However I don’t believe that business can be completely ethical especially in price determination. This is because pri ces are determined by the market with all organization trying to make the most profits. The code of ethics is crucial for an organization as it leads to cultivation of good behaviors such as accountability honesty and integrity which makes the organization not to operate smoothly. Legal considerations are crucial because it save an organization or individual trouble with the law. For instance nurses are expected to abide to the rule of confidentiality of their patient (Brenkert & Beauchamp, 2010 618). If they have information about a HIV positive patient and discover that he/she plans to have sexual relations with a HIV negative partner they cannot blow the whistle since they can be sued. Scenario Three Increasing women in the top executive positions increase diversity in the board of directors’ composition. This creates an arena for discussion of different perspectives on issues which helps in making good decisions. Lord Davies report has recommendation on how women represen tation in top executive position in UK can reach to 25% by 2015. The institute of leadership report on women reveals that despite about half of the working population consist of women they are underrepresented in the top executive positions. Women hold only 12% of directorship position and only 22% of top management positions. Barrier to female occupation of top position are gender biases and the fact that women who are also homemakers are unable to give total commitment to work such as working long hours. Promotion today is based on performance. The first wave of feminism started in the late 19th century to early 20th century. This was during the industrialization era and the wave had the aim of pushing for opening job opportunity for women. It challenged the culture of domesticity calling for women representation in the political arena. The second wave was in the 1960s-90s. This came after the civil movement had diet down. The main aim of this was the recognition of female reprodu ctive rights and promotion of equal social rights. The third wave which is also called post feminism started in the 1990s to date. This is where female portray their sexuality by wearing high heels pushup bras and make up (Vinnicombe, 2008; 142). They assert that one can be beautiful and at the same time have brains. In the former waves female sexuality was seen as an object of oppression but it is now viewed as a subject of feminine beauty. Scenario four The stakeholders theory outlines haw an organization should be managed and the ethical

A Teachers View On Teaching Kindergarten English Language Essay

A Teachers View On Teaching Kindergarten English Language Essay Kindergarten teachers establish the foundation of all education. These extraordinary educators help their students learn the alphabet, how to count, and how to write; all the qualities needed to be successful in school. In addition to academics, kindergarten teachers are instrumental in setting standards for good behavior in school. Without their guidance the children would not have the proper foundations for their future learning. Kindergarten classrooms and teachers are very important to little children who are just beginning their formal learning process at a new school. Kindergarten teachers are the most important in a childs education. Kindergarten is the second stage in school following pre-kindergarten. In pre-kindergarten you learn how to get along with and play with other students. Kindergarten is the establishment of young childrens existence in the educational system. What does the word kindergarten stand for? It means a school or class for children usually from four to six year olds à ¢Ã¢â€š ¬Ã‚ ¦ that serve as an introduction to school. (Merriam-Webster) Some teachers said it is not an easy job teaching kindergarten students. Two teachers interviewed say teaching kindergarten is a difficult job. Mrs. Van Dyke stated, Yes, yes, yes!! I really enjoy teaching them, but every day presents its own trials. It also has many rewards, (Mrs. Van Dyke). Mrs. Byrd stated, The good thing about kindergarten is the children are enthusiastic to learn and strive to please their teachers. I like being able to be the one that teaches the establishment of letters, phonics, numbers, and reading comprehension, (Mrs. Byrd). Mrs. Van Dyke and Mrs. Byrd where asked what inspired them to become a teacher? Mrs. Van Dyke said, I have always loved children. I began working as a dance teacher and enjoyed it so much I decided to go into it as a career, (Mrs. Van Dyke). Mrs. Byrd stated, I started working in the school system so that I could spend more time with my two sons. I worked three years in second grade. My Assistant principle moved me to kindergarten becau se she said my gift was really with the little ones, (Mrs. Byrd). Without the teachers the kindergarten class would not happen. The teachers will help the students to get all of the foundation needed to go on to the first grade. In essence, kindergarten teachers are very important to a little childs educational career. In an interview, Mrs. Van Dyke and Mrs. Byrd were asked how long it took them to complete their degrees to become a teacher and teacher assistant. What degree(s) did they get from college, and what college(s) did they attend? Mrs. Van Dyke stated, It took me four years. I took classes during the summer and graduated in four years. I attended Harding University and Slippery Rock College, receiving a degree in early childhood education, (Mrs. Van Dyke). Mrs. Byrd said, I have an associates degree in computer science from Gaston College. I worked full time in a textile mill so it took me between three to four years to complete it, (Mrs. Byrd). A classroom is a place for learning experiences. Most kindergarten classrooms have a kitchen play house set. Also the classroom contains water paint, a computer, a sand table, blocks, puzzles, and a writing center. These activities allow students to interact with each other students in the class. In a kindergarten classroom you have cubbies to store students supplies (book bag, clothes and other stuff). Also you will find a smiley chart which is used to display students behavior for the day. It is called a behavior chart; this chart is a scale showing a range of behaviors from high spirits to low or disappointing behavior from a teachers point of view. Lesson plans are a teaching tool to show how a teacher gets ready for his or her class every day. Lesson plans show what teachers do to help each and every student. Carpet time in kindergarten classes is a learning period. During carpet time the kindergarten students learn the days of the week. That is very important for little children to know the days of the week. Also during carpet time the children sing the good morning song. Here are the words to the song; Good morning to you! Good morning to you! Were all in our places with bright shining faces. Oh, this is the way to start a great day! Good morning to you! Good morning to you! Were all in our places with food on our faces. Oh, this is the way to have a great day! Good evening to you! Stars and the moon in their places they go through their paces. Oh, this is the way to end a good day! (Variety of Kindergarten Choices Increases). Also while the children are at the carpet the sing songs and move around the carpet or rug in the r oom. It is very significant that the children know the days of the week, how to count, and read previous to first grade. Every now and then when the students are misbehaving they do not get to go outside and play with other children. That is called a time out. Some children do not like that at all. Also when some of the students misbehave they have to pull a clip. That is one way to tell when a student is being terrible. All of the children love to be interactive. [The little students will be devoted to this lesson because they are interactive in on the increase their class tree and then take an interactive piece in putting their letter on the tree when it is their turn to put their letter on the tree.] That is very full of life measurement in that days lesson plans. All most all of the kindergarteners are not able to sit in their sits all day long, they need to get up and be in motion around sometimes. If you have something in your lesson this is a good song to use. This is how the song goes like this. [Inside, outside up and down long and short smile and frown hot and cold fast and slow how many opposites do you know Were alert when its morning and sleep when it is night. We keep close to home will not go far out of sight. The children try to be good and not to be bad. Were a good quantity are often in high spirits, but sometime our toys are profound but some are light too. Our toy box is sometimes unfilled when were having an enjoyable time playing with toys. But its full again when we shipshape up at the end of every day.] That is one way to get their small bodies moving, and the kindergarteners will not be so wiggly when youre ready to be knowledgeable. In kindergarten the students may also have some home work to do. The students may have home work is really not difficult. At the start of the school year, the teachers will help the students learn how to say and write their alphabet. Some say that is too much on a little kindergartener. But it is really not. Students have to know the alphabet so when they get to first grade. They are the building blocks needed throughput their educational career. In addition to songs, nursery rhymes are another way to get the students active. Here are two examples of nursery rhymes, twinkle, and twinkle, and little star, and Hickory, dickory, dock. Hickory, dickory, docks; the mouse ram up the clock. The clock struck one, and the mouse ran down the clock, Hickory, dickory, dock (Mrs. Byrd). Twinkle, twinkle, little star, how I wonder what you are! When the blazing sun is gone, when nothing shines upon, than you show your little light, Twinkle, twinkle, all the night. Twinkle, twinkle, little star, how I wonder what you are! Then the traveler in the dark thanks you for your tiny sparks; he could not see which way to go, it you did not twinkle so. Twinkle, twinkle, little star, how I wonder what you are! In the dark blue sky you keep, and often through my curtains peep, for you never shut your eye till the sun is in the sky. Twinkle, twinkle, little star, how I wonder what you are! As youre bright and tiny spark lights the traveler in the dark, through I know not what you are, twinkle, twinkle, and little star. Twinkle, twinkle, little star, how I wonder what you are! (Mrs. Van Dyke). Those are really good nursery rhymes, and the children will love to say them and read them all the time. The alphabet comforter is a good thing to use because it refreshes their memory allowing them to remember their sounds and how to pronounce them; some teachers say this lesson is great for little ones. To help the students count, the teachers can use some number word rhymes to help them remember how to count. The teachers also can help them to remember their colors by doing color rhymes or songs that tells them how to spell the colors of the rainbow. Here is one of the color rhymes for the color black. B-l-a-c-k spells b-l-a-c-k. B-l-a-c-k spells b-l-a-c-k. Scary cats are b-l-a-c-k. Flying bats are b-l-a-c-k. Santas boots are b-l-a-c-k. I like b-l-a-c-k. B-l-a-c-k spells b-l-a-c-k. B-l-a-c-k spells b-l-a-c-k. Sunday shoes are b-l-a-c-k. Jelly beans are b-l-a-c-k. B-l-a-c-k spells b-l-a-c-k (Mrs. Van Dyke). B-r-o-w-n, b-r-o-w-n thats how you spell b-r-o-w-n, b-r-o-w-n. Big trees outside are b-r-o-w-n. B-r-o-w-n Hersheys- kisses are b-r-o-w-n. (Mrs. Byrd and Mrs. Van Dyke). Another method of learning is where the teacher begins by trying to activate prior comprehension is. The teachers questions will help them to understand what they will be learning. The teacher will encourage students to start developing skills in listening to others, sharing thoughts or a dream, thinking about what they know, thinking about what they would like to know, and following directions. The teachers will also assist students in developing a positive reception for other ideas. A positive reception for the topic they will be studying. A feeling of accomplishment. Core curriculum content standards; all students will get your hands on historical understanding of societal thoughts and forces throughout the history of New Jersey, the United States, and world. Introduction; review; the teacher will ask the students what they are on familiar terms with about communication. Enthusiasm the teacher will have books, fiction and nonfiction, displayed on the topic. Predicament what so we already know about communication and what do we want to know? Development; the teacher will tell the class that they will be studying about communication. Ask the class what they think communication is. The teacher will ask the class what types of things they would like to be familiar terms with about communication. The teacher will go over the responses he or she has written on the paper and put it into simple words. The teacher will explain the different things they will be learning with reference to ways communication happen, inventions, a nimal communication by Aliki, graphic representation document. (Mrs. Van Dyke). All classrooms and teachers can be very different than others in the same school. Also all most all of the teachers have a different way they teach their class. Some students may or may not like the way the teacher teaches, that is very okay. This is why kindergarten teachers and classroom in a childs educational career. Life as a kindergarten teacher can be very hard in a way. The teachers have a very big job on their hands because teaching kindergarten is hard knowing what that child goes through at home. Some parents just do not care about their childs school work. So with that being said it is very hard sometimes to be a teacher. The teachers will never know how a child is treated at home unless they tell you. So kindergarten teachers are so very important in a childs educational career. It is exceptionally okay that a child goes to pre kindergarten taking place before he or she goes off into kindergarten to establish on his or her educational career. The teachers will be the only way a child will get through school. That is why kindergarten teachers and classrooms are so important in a childs educational career. Byrd, Lisa. Personal interview. 20 march 2009. Kindergarten. Merriam-Webster Online Dictionary. 2010. Merriam-Webster Online. 5 January 2010 Vandyke, Suzanne. Personal interview. 11 Mar 2009. Variety of Kindergarten Choices Increases. 24 Jan 2009:

Where Will They Burry Your Heart :: essays research papers

Where Will They Bury Your Heart? I have always found profound inspiration in the stories of men and women who lived and died for Christ. In fact, their incredible level of commitment is a measuring stick for my life; their undying courage is a source of my encouragement; and their burning passion is the light to my personal mission. Where would I be without the stories of these seemingly ordinary people who behaved extraordinarily against impossible odds? My faith is lifted each time I recall these true heroes. For me, one of the most moving is the powerful story of David Livingstone and the sacrifices he made to open the great continent of Africa to Christianity. When I first heard this story, I was already very familiar with the hardships that missionaries regularly endure. But the day I heard Livingstone’s story, I was finally able to embrace the extreme price one man paid. Travel with me to the year 1857. David Livingstone had already lived in the land of, â€Å"the thousand villages where no missionary has ever been† for sixteen years. He is now back in England, ready to address Cambridge university students. The custom of the time is for the students to heckle the speaker—all in fun. This day is no exception. The students have peashooters and noisemakers of every description. They’re ready for whoever this man might be. Then David Livingstone slowly walks to the podium with the step of a man who has walked 11,000 miles. His left arm hangs dead at his side, having been nearly ripped from his body by a lion, his shoulder crushed into splinters. His skin is a dark, leathery brown from sixteen years in the African sun. His face is furrowed with innumerable lines from bouts with African fever, which have also racked and emaciated his body. His physical being is wasted. He is half deaf from rheumatic fever and half blind from a tree branch that whipped him in the eyes while traveling through the jungle. The students are staring. They know this is not just another guest speaker. Before them is a man to be taken seriously. This is a life that was literally being burned out for God. As he begins to speak they learn that Livingstone’s journey began as a young man in Scotland. It was there that he prayed, â€Å"Lord, send me anywhere, only go with me. Lay any burden on me, only sustain me.

Linear Programming in Finance, Accounting and Economics

Linear Programming in Finance, Accounting and Economics Sijia Lu 7289928683 Abstract This article is literatures review about five articles, which apply linear programming to Finance, accounting and economics. The mathematical method is found of crucial importance in those fields. The paper shows how theoretical inference in linear programming throws light upon realistic practice, and how empirical evidence supports those theories. Keywords: finance; accounting; economics; linear programming; investment analysis Linear Programming in Finance Application of Linear Programming to Financial Budgeting and the Costing of Funds† explored how to allocate funds in an enterprise by applying linear programming. As Charnes, Cooper and Miller analyzed, at least three problems are to be considered to solve the allocation problem: 1) Plans for production, purchases, and sales under certain structure of the firm’s assets, in order to maximize its profit or reach other objectives. 2) Th e change of the firm’s profit per unit change in the structure of the assets. 3) Opportunity cost of the firm’s funds.The article starts with a simple example with one commodity and one warehouse. Let B be the fixed warehouse capacity, A be the initial stock of inventory in the warehouse, xj be the amount to be sold in period j, yj be the amount to be sold in period j, pj be the sales price per unit in period j, and cj be the purchase price per unit in period j, then we have due to the cumulative sales constraint; due to the warehouse capacity constraint; due to the buying constraint; due to the selling constraint; and with our goal of maximizing The dual problem is also obvious.It is to minimize subject to and to where As we learned, â€Å"dual theorem of linear programming† says that the two optimal values of the original problem and the dual problem should be equal. Using this theorem, the authors then reached a new method of evaluating assets. Because , we h ave in which the two sides must have the same units of measure. So it is now obvious that t*k represents the value per unit of net warehouse capacity and u*k represents the value per unit of initial inventory in the warehouse. Similarly, consider the financial problem, which has liquidity constraints as here j-? represents payments and j-r represents receipts, M0 is the initial cash available and M is the balance the firm desired the maintain. By examining the dual problem of this, we can find corresponding dual variables for the problem called, say, vk. Again, from the equality we found before, we can learn that the two sides of the equation have the same units of measure. It is then seen that the v’s should be dollars per unit time per dollar invested. The valuation of assets or investments is of crucial importance to any business.So far, by simply applying the dual theorem, Charnes, Cooper and Miller have created a new method of evaluating assets or investments. This metho d of evaluating is also easy to find out answers. It is intelligent to examine the units of measure rather than try to solve the specific problems. The interesting thing is that in realistic problems, we can find true meanings of theoretical dual variables. Then the authors mixed the two former problems together to see a more realistic case – a warehouse problem with financial constraints.So the following new constraints are added: Now if we define We’ll get the new dual problem: Here, V1 is the incremental cumulative internal yield rate. Or it is the opportunity cost the capital invested – â€Å"it shows the net amount to which an additional dollar invested in the firm will accumulate if left to mature to the end of the planning horizon. † This is also easy to understand in terms of economics, maximizing profit can be the same as minimizing the opportunity costs. The article then went through several practical problems using the dual variable evaluating method.It is also interesting to find out that all the commodities are directly linked to the funds-flow while the goods-flow can be avoided in the warehouse problem with multiple commodities. An Example â€Å"A linear programming model for budgeting and financial planning† created an accounting experiment in which the dual variables introduced earlier were calculated which can also be considered as a sensitivity analysis. This can be seen as application and verification of Charnes, Cooper and Miller’s earlier theory. In the linear programming problem listed below, (1) represents the interests earned with a rate of 0. 29%; (2) holds because firm’s sale of securities will not be more than the beginning balance of this amount; (3) represents the maximum collection of receivables will not exceed the beginning balance of account receivable; (4) means the initial cash balance constraints the purchase of securities; (5) indicates â€Å"contribution† on a unit s ale per unit deduction from the ending goods inventory, with prevailing selling price being $9. 996 and cost of production $2. 10; (6) holds because of the cost structure: in the $2. 10 cost, $1. is the material cost and $1. 1 is the conversion cost (direct labor cost and direct overhead); (7) represents the production capacity limits by limiting the value of raw materials; (8) holds because conversion is also limited to raw materials at the beginning of the period; (9) means market limit to the sales by constraint on the standard cost; (10) means sales are also limited because it can not be more than the beginning balance of completed goods; (11) represents the repayment of loans will not exceed the beginning balance of outstanding loans. 12) indicates the limit of accounts payable; (13) is the depreciation charge equation with a rate of 0. 833; (14) indicates the structure of costs to be incurred in the current period, including fixed expenses ($2,675,000), variable cost, effectiv e interest penalty for discounts not taken on accounts payable (at a rate of 3. 09%), and interest on loans (at a periodic rate of 0. 91%); (15) represents income tax is accrued at 52% of net profit and the dividend equals to $83,000 plus(minus) 5% of the excess(shortage) of the expected profit, $1,800,000; (16) is the limit of minimum cash balance required by the company policy; (17) holds because an expected price rise in the next period leads the company to decide the ending inventory should be at least the minimum sales expected in the next period; (18) means ending materials must be sufficient for the production of next period; (19) is the payment limits: all income taxes payable and dividends must be paid by the end of current period.And because we can considers our goal as maximizing net additions to retained earnings, we have substitute the K’s with figures of balance sheet, which is showed below, we can calculate the X’s As we learned before, a dual evaluator indicates the change in net addition to retained earnings if the constraints corresponding to the given evaluator were relaxed by one dollar. For example, the dual evaluator of (7) is $3. 594936. This means that if production capacity ere increased in case that exactly one additional dollar’s raw material is used, the retain earnings will increase $3. 94936. To see this case in detail, table 5 shows what happens after altering the firm’s raw material processing capacity by one unit. Additional cash can be obtained in 3 ways: a) selling securities; b) borrow from a bank; c) delay payment on account payable. But the cheapest way is a). Thus we can calculate the opportunity cost per dollar by: the firm loses interest income of $0. 00229 of every dollar of securities sold while savings from taxes and dividends can relieve this loss, calculate the periodic loss, it is $0. 00104424. Evaluate this loss from an aspect of infinite periods:Apply this to the last step of deductio n, we get $3. 594936, again. Our former inference is thus confirmed. Not only from the mathematical aspect but also from the accounting aspect. In this case, linear programming offers a highly flexible instrument. As in the case, â€Å"all sensitivity changes within any specific part of the model are evaluated in terms of their effect on the entire model. † It is also highlighted, as we mentioned above, this kind of evaluation can be done without actually solving the entire problem. Thus this method is not only reasonable but also convenient.Linear Programming in Economics So far we have seen the application of linear programming in the field of finance and accounting. Now let’s see an interesting example which apply linear programming to economics. A linear program can approximate product substitution effects in demand. In general, the demand function may be written as (1) where p is an N * 1 vector of prices, q is an N * 1 vector of quantities, a is an N x 1 vector o f constants, and B is an N x N negative semidefinite matrix of demand coefficients. And the objective function for the competitive case can be written as maximize 2) where c(q) is an N * 1 vector of total cost functions, q >= 0, AND Substitute (1) into (2) We have the new objective function Maximize (3) In economics, we know that the total welfare of transactions can be separated into two parts: consumers’ surplus and producers’ profit. In mathematics, these two parts can be written as We also represent the resource scarcity by adding constraints (4) The Kuhn-Tucker conditions, which are necessary (but not su? cient) for a point to be a maximum are: Thus the Kuhn-Tucker necessary conditions for the original problem are equation (4) plusFor monopoly market, the object function is a little different, it is to Maximize (5) while the Kuhn-Tucker necessary conditions are equation (4) plus From the competitive market objective function (3) and the monopoly market objective f unction (5), we can see that both involve a quadratic form in p. In order to set up the LP tableau, define a function representing the area under the demand curve as (6) And the total expenditure function as (7) Then we can derive the following figure for (6) and (7): The representation of the piecewise linear approximation in LP is shown for the two-good, separable-demands case, in table 1. here costs for the ith product in the jth activity producing it are represented by cij; unit outputs of the ith product in the jth activity producing it are given by yij; The quantities sold of the ith product corresponding to the endpoint of the jth segment are defined as qj; Values of W for the ith commodity corresponding to the amount sold, qj, are given by wij; Values of R for the ith commodity corresponding to the amount sold, qj, are represented by rij; The target level of producer's income is denoted by Y*.Note that the LP problem has its certain properties. In table 1, no more than two a djacent activities from the set of selling will enter the optimal basis at positive levels. And also, by use of the function R in the constraint set, the model includes a measure of income at endogenous prices. The article then looks into a more complicated case where there exists substitution of demands. That is, one good’s demand can be substituted by the other one’s.An assumption, as the basis of the approximation procedure developed for this situation, is that commodities can be classified into groups, which allow the marginal rate of substitution (MRS) to be zero between all groups but nonzero and constant within each group. Then consider a group consisting of C commodities. We can create table 3 for the situation: The authors pointed out that â€Å"each of the blocks of activities [W's R's -Q's 1] constitutes a set of ‘mixing’ activities for one segment of the composite demand function for the commodity group†. i. e. [W's R's -Q's 1]T=Relative prices of commodities in the group are assumed fixed, both within and between segments, and are defined by Also define the quantity index as and price index as where Then we create table 4, which is a simple extension of the single product case. Only the selling activities are shown. in which The price-weighted total quantity is (8) To extend the case of demand in fixed proportions within a group, define matrix A as The elements in matrix Q can now be calculated as (9) substitute (8) into (9), we have The price-weighted total quantity, q*sm, is given by so (9) is equal to hen calculate the elements of W and S Now we are able to calculate the MRS By rearranging we get MRS=-p2/p1, the required result. An Expansion The use of linear programming in the field of economics was continued in the paper â€Å"Endogenous Input Prices in Linear Programming Models†. In this paper, the author provides a method for formulating linear programming models in which one or more factors have upw ard sloping supply schedules, and the prices are endogenous. Instead of examining the demand function, Hazell starts from the function of the producers, whose goal is to maximize their profit here x is a vector of output levels; p and c are vectors of market prices and direct costs, respectively; d is a vector of labor requirements; L is the amount of labor employed at wage w. Now if the buyer of labor is monopoly, or the market is a monopsolistic market,due to economic definition we’ll have Then the problem becomes Again we use Kuhn-Tucker conditions to solve for the optimal solution. L;0, so we have = w+? L Thus, given the optimal amount of labor used (L*), the associated market-clearing wage is w* = a + PL*, and this is smaller than ? by PL*.This is correct by intuition and empirical evidence. Similarly, if the situation is competitive market , we can derive? =w, which is quite different from the former case. Using the method of Duloy and Norton, Hazell calculate the suppl y curve of labor, which is actually a stepped function, showed as below: Hazell pointed out that â€Å"stepped supply functions arise artificially from using linearization techniques, but they also arise in reality when different sources of labor are identifiable which can be expected to enter the labor market as the wage reaches critical levels. And then he also mentioned another way to find out the supply function of labor. This article is a development and application of the former article. The method for achieving these results utilizes the sum of the producers' and consumers' surplus, and is an extension of existing methods for solving price endogenous models of product markets. Linear Programming in Daily Investing Linear programming is such a useful tool that we can find its advantages in finance, accounting and also economics. But what about in our daily life?How can linear programming help when we make decisions about our own investing, say, our own financial portfolios in various stocks? In 2004, C. Papahristodoulou and E. DotzauerSource wrote an article about these questions, named â€Å"Optimal Portfolios Using Linear Programming Models†. This paper is about three models: The classical quadratic programming (QP) formulation and two new ones — (i) maximin, and (ii) minimization of mean absolute deviation. The first model is to s. t. where i and j are securities; ?ij is the covariance of these securities; xj is the portfolio allocation of security j.These are the variables of the problem and should not exceed an upper bound uj; ? is the minimum (expected) return required by a particular investor; and B is the total budget that is invested in portfolio. The second model is established so the minimum return is maximized. Regarding the constraints, one might assume that every period's return will be at least equal to Z. For period t, this constraint can be formulated as: where rjt, is the return for security j over period t. The third mod el simplifies the Markowitz classic formulation is to use the absolute deviation as a risk measure.It is proved by Konno and Yamazak that â€Å"if the return is multivariate normally distributed, the minimization of the mean absolute deviation (MAD) provides similar results as the classical Markowitz formulation†. And as is known, MAD is defined as We define first all Yt >0 variables,t = 1, †¦ ,T. These Yt variables can be interpreted as linear mappings of the non-linear Thus, the objective function is to minimize the average absolute deviation and the constraints added are Then the author tested all three models, using monthly returns from 67 shares traded in the Stockholm Stock Exchange (SSE), between January 1997 and December 2000.As expected, the maximin formulation yields the highest return and risk, while the QP formulation provides the lowest risk and return, which also creates the efficient frontier. The minimization of MAD is close to Markowitz. The results are as follows: All three formulations though, outperform the top equity fund portfolios in Sweden. They also conclude, â€Å"When the expected returns are confronted with the true ones at the end of a 6-month period, the maximin portfolios seem to be the most robust of all. † Conclusion We have seen the crucial importance of linear programming to finance, accounting, economics and also our daily life.It turns difficult problems into easier ones. By using this mathematic way of solving problem, we can achieve more intelligent choices while wasting less. The study of linear programming is so useful that in the future, it will hopefully find more use in the world of economics and management. References â€Å"Application of Linear Programming to Financial Budgeting and the Costing of Funds†, A. Chares, W. W. Coopers, and M. H. Millerss, The Journal of Business, Vol. 32, No. 1, Jan. , 1959 (pp. 20-46) â€Å"A Linear Programming Model for Budgeting and Financial Planning†, Y. Ijiri, F. K. Levy, and R. C.Lyon, Journal of Accounting Research, Vol. 1, No. 2, Autumn, 1963, (pp. 198-212) â€Å"Prices and Incomes in Linear Programming Models†, John H. Duloy and Roger D. Norton, American Journal of Agricultural Economics, Vol. 57, No. 4, Nov. , 1975 (pp. 591-600) â€Å"Endogenous Input Prices in Linear Programming Models†, Peter B. R. Hazell, American Journal of Agricultural Economics, Vol. 61, No. 3, Aug. , 1979 (pp. 476-481) â€Å"Optimal Portfolios Using Linear Programming Models†, C. Papahristodoulou and E. Dotzauer, The Journal of the Operational Research Society, Vol. 55, No. 11, Nov. , 2004 (pp. 1169-1177)

Eric Whitacre Biography

Eric Whitacre is one of the most well known, performed, and awarded choral composers in the modern day choral scene. Eric was born on January 2, 1970 in Reno, Nevada, dabbling in piano lessons as a child and later, in junior high, joining marching band, and playing synthesizer in a techno-pop band. Believe it or not, Eric dreamt of becoming a rock star. (Bowen) Although he is not among the likes of Metallica or The Beatles, Eric has won a Grammy for Best Choral Performance for his album â€Å"Light and Gold† in the past year, as well as a nomination in 2007 for â€Å"Cloudburst and Other Choral Works†.He is the youngest recipient ever of the Raymond C Brock Commission given by the American Choral Directors Association, awarded in 2001, as well as numerous other awards from the ACDA, the Barlow international composition competition, and American Composers' Forum. (Official Website Biography) Although Whitacre is known for his choral works, he also writes and composes for wind ensembles, full orchestras, a full musical titled â€Å"Paradise Lost: Shadows and Wings†, as well as pieces for solo voice and supporting instrumentals. The most known piece that Eric has composed is the acapella choral piece titled â€Å"Sleep†. Sleep† is a SATB choral piece. The story behind this haunting song is that Julia Armstrong, a lawyer and professional mezzo-soprano from Texas, wanted commision Whitacre to compose a choral that would be performed by the Austin ProChorus, where she was an avid member of the choir. She wanted the piece to be a memorial of her beloved parents, who died within weeks of each other after fifty years of marriage. She wanted the piece to use the poem by Robert Frost, called Stopping By Woods on a Snowy Evening. Whitacre agreed to take on her request and was deeply moved by her story.Unfortunately, after a careful composition by Whitacre and a breathtaking performance of the piece by the Austin ProChorus, Robert Frost's e state forbid Whitacre from using the poem in any way for the piece. The poem will become public domain in 2038, but he did not have that long to wait as other directors were practically begging to use the piece for their choirs. Instead of letting the piece â€Å"lie under his bed, dead†, as Whitacre said, he talked it over with his wife and decided to ask his friend and poet Charles Anthony Silvestri to compose a poem to set words to the iece. Silvestri was a trusted lyricist for Whitacre, writing lyrics for Leonardo Dreams of His Flying Machine, Lux Aurumque, Nox Aurumque, and Her Sacred Spirit Soars, all celebrated Whitacre pieces. Tony incorporated a lot of the same ideals of Stopping By Woods on a Snowy Evening, the biggest being ‘sleep'. Whitacre says that he loves Tony's poem more than he ever did Stopping and will never set the words to Frost's poem to his song, even when it becomes available in 26 years. (Whitacre) The piece itself is musically exquisite.It gra bs your attention almost immanently. Whitacre uses this method of stacking voices at crucial points in the plot by splitting every voice part into two parts, so what was a four part becomes an eight part. The texture and the dynamics are maticulously planned and formulated, as if Whitacre were sitting there telling a story about a personal experience, but the choir was doing the speaking for him. There are moments when you can feel the pain and anguish he wanted to express just through the dynamic of the voices. The emotion of this piece is palpable.The lyrics read: â€Å"The evening hangs beneath the moon A silver thread on darkened dune With closing eyes and resting head I know that sleep is coming soon Upon my pillow, safe in bed, A thousand pictures fill my head, I cannot sleep, my minds aflight, And yet my limbs seem made of lead If there are noises in the night, A frightening shadow, flickering light†¦ Then I surrender unto sleep, Where clouds of dream give second sight. What dreams may come, both dark and deep Of flying wings and soaring leap As I surrender unto sleep As I surrender unto sleep. † (Official Website)The last few bars of the piece are of the sopranos holding the word â€Å"sleep† and the other voice parts singing â€Å"sleep† in a two note pattern, growing quieter and quieter into absolute silence. I believe that the song, in its core, is about death. Perhaps, Silvestri wrote the piece with someone in mind who was very sick and their death came as a relief, almost as sleep does at the end of a very long and tiring day. Whitacre does something in his music that is so unique and complex, it is almost hard to believe that he did not know how to read music when he attended the University of Nevada as a Music Education major. Bowen) The way that he builds chords to provide moments of tension is seventh or ninth chords, with or without suspended seconds and fourths and root-position major triads with an added major seco nd and/or perfect fourth. (Shrock) Whitacre also uses unconventional chord progressions, meter changes, and harmonies. He is also known to use hand actions or props, as he does in the piece â€Å"Cloudburst† when the singers use snapping, clapping, and stomping to imitate the sound of a rainstorm.With all of that being said, Eric has almost nothing in common with other composers of our time, and honestly that is what gives him so much of an edge. He is willing to step out of the box and be daring and different and that risk has paid off. Works Cited: Bowen, Meurig. â€Å"Whitacre: Offical Biography. † Web article. (2006): n. page. Web. . â€Å"Official Biography. † Official Website. n. page. Web. . Whitacre, Eric. â€Å"The Story Behind Sleep†. Official Website. Web Article. (The song can be heard on this link) Shrock, Dennis (Mar 2009). Choral Repertoire. Oxford University Press (USA). p. 761. ISBN 978-0-19-532778-6.