Organizational Behavior discusion assignment Example | Topics and Well Written Essays - 3000 words

Organizational Behavior discusion - Assignment Example The Hawthorne legacy has had a strong influence in today’s workplace by setting the standards for managers to view people not as machines but as humans and attend to their individual needs; offers supportive leadership at the work place rather than pushing for results (Kinicki & Kreitner, 2006). McGregor’s Theory X assumes that most people dislike work and try to avoid it when they can, therefore they must be coerced and threatened in order to work. Theory Y on the other hand says people like work as it is a natural activity like rest or play and people are capable of self-control and self-direction when they understand the goals. Theory X goes ahead to assume that people prefer to be directed and tend to avoid responsibility and that they are only interested in security. Theory Y on the other hand people get committed when they are rewarded for it and that they will learn and seek responsibility as they are imaginative and creative. It is hard to work under Theory X ma nagers as most of them only stress on work and more work without understanding employee needs. I prefer the Theory Y managers because they understand people and they are concerned about creating positive relations that foster productivity in the organization (Kinicki & Kreitner, 2006). C. The term E-business is defined as the use of the internet to more effectively and efficiently manage every aspect of a business. Employees today have acquired skills in many areas of digital communications and these include the use of blogs, emails, social networking and other sites where users provide and refine content. In this kind of environment therefore where the employees have the control over the information that they can share and access, the role of the manager is evolving into one that aims at providing the means for collaboration that is they learn the need for team work and empowerment in independent decision making (Kinicki & Kreitner, 2006). 2. A. There are three layers of organizati onal and these include: (1) observable artifacts which are the physical manifestations of an organization culture such as manner of dress, acronyms etc. ; (2) espoused values which are states values and norms preferred by an organization; (3)basic underlying assumptions which are the things taken for granted but guide organizational behavior. There are four functions of organization culture: (1) organizational identity; (2) Collective commitment; (3) social system stability; (4) it acts as a sense making mechanism (Kinicki & Kreitner, 2006). There are four types of organizational culture according to the competing value framework each with distinct characteristics. The first is a clan culture and this has an internal focus and values flexibility: it uses employee involvement as a method of achieving flexibility. The second is an Adhocracy culture which has an external focus and values flexibility. This culture values innovation and fast responses to change. The third is a market cul ture which has a very strong external focus valuing stability and control. They are majorly driven by competition and put emphasis on customer satisfaction. The fourth and last category is the hierarchy culture that has an internal focus valuing stability and control: it lays emphasis on formal structured work in order to meet high standards (Kinicki & Kreitner, 2006). B There exist six socialization tactics used by organizations to socialize employees. Each of the tactics provides an organization with two

Transcontinental railroad Term Paper Example | Topics and Well Written Essays - 2500 words

Transcontinental railroad - Term Paper Example Such policies are implemented by regulatory authorities through budgets and other rules and regulations. However, there are some factors that affect the economy on the very basic level. One of those factors is infrastructure of a country. Infrastructure of a country can play an important role in the strengthening of the economy of a country. This paper analyses one such example of the effects of infrastructure on the economy. The example is that of the First Transcontinental Railroad. This railroad is said to be the first communication revolution of America. The railroad reduced the time of travel between east and west costs from six months to one week and it was indeed a huge achievement. This paper examines the problems faced by the entities engaged in the construction of the railroad and the effects of the railroad on the economy of the country (Heintz, 2009). Infrastructure can enhance the growth of the economy of a country at a very fast pace, specifically in case of developing countries. Developing companies usually have weak economic environment because of lack of sufficient infrastructure. Infrastructure can boost trade in a country which results in accelerated economic activities in the country. This scenario can best be explained with the example of the First Transcontinental Railroad that was constructed between the years 1863 and 1869 in the United States of America. The railroad was built by the Central Pacific Railroad of California and Union Pacific Railroad. These two entities were chartered by the Pacific Railway Act, 1862. This railroad connected the already developed railway network of the Eastern cost with California that was in its developing stages. The railroad was completed in May, 1869 when it changed the economic scenario of the American West for good. The railroad initiated a new series of trade and communication that triggered the economic growth in the USA. Planning for Construction of the Transcontinental Railroad In the year 1862, it was determined that the companies that would carry out the construction of the Transcontinental Railroad would be Central Pacific Railroad and Union Pacific Railroad. The companies started construction from their respective points. Central Pacific started building the railroad eastward from Sacramento, California and Union Pacific started building the railroad westward from Council Bluffs, Iowa. Although the companies had been assigned the task and they had started constructing the railroad, the point where both the railroads would meet was not determined. There were a number of problems that hindered the construction of the railroad resulting from the lack of adequate planning. The construction also slowed down due to the Civil War between the years 1861 and 1865. This factor also added to the problems already present due to the lack of planning. However, a point in the Mormon territory of Utah was determined to the Promontory Point where the railroads being constructed by the two companies would meet. The construction completed on 10 May, 1869 when the two railroads met at the Promontory Point. Problems Faced in Construction A railroad connecting the east and west cost of the USA had always been a dream but it was shaped into reality by the President Abraham Lincoln. However, the railroad was completed after four years of his death. The construction of the railroad was not independent of any problems. There were a num

lawmaking process in the parliament

lawmaking process in the parliament DESCRIBE THE PHASES OF THE LAWMAKING PROCESS IN THE PARLIAMENT. IN WHAT CIRCUMSTANCES CAN PROPOSED LEGISLATION GO FOR ROYAL ASSENT WITHOUT THE APPROVAL OF THE HOUSE OF LORDS? The Parliament of England as one of the main pillars of a constitutional democracy plays a vital role in governing the country by lawmaking, the process which divides into number of stages. These stages which comprise the first reading, the second reading, the Committee Stage, the Report stage, the third reading, the approval of the House of Lords and the Royal Assent will be main focus of this essay. In addition, the essay will concern rather exceptional situations when proposed legislation might go for Royal Assent without, otherwise necessary, approval of the House of Lords. The Parliament of England stems from royal council which was established by William the Conqueror in 11th century and had further developed in 13th century with issuance of Magna Carta as a result of struggle for limit of the power of the English monarchy and thus is crucial for separation of powers an important thrust of the constitutional monarchy. Over the centuries, the Parliament has evolved into the highest source of law in the UK. The concept of Parliamentary Supremacy was introduced by English constitutional theorist Albert Dicey at the end of 19th century. The modern Parliament consists of three elements, the House of Commons, the House of Lords; and the monarch each of which has its own function in lawmaking process. Members of the House of Commons debate the issues of the proposals for new laws while members of the House of Lords are responsible for making laws and investigating political issues. The lawmaking process is a complex procedure which starts with pre-parliamentary process by identification of policy objective which included in a Green paper, a document that puts forward the proposals on which the parties give their opinions and views. The Green Paper is followed by a White paper which consists of the reform plans. Further, a Bill must be given tree readings in both in the House of Lords and the House of Commons. The procedure can be commenced in either House and it starts with the first reading which is purely a formal procedure when the title of the proposed Bill is prepared, read out and followed by an order to be printed. Next step is the second reading which usually takes place no sooner than two weekends after first reading. It is the main point in the process and during this phase main provisions of the Bill are discussed. At this stage the proposals may be amended and it is up to the members to decide whether the legislation should proceed and they do it by exercising their voting rights. Once second reading is complete, the Bill goes to the Committee Stage which usually starts within a couple of weeks after a Bills second reading. At this stage the detailed examination, clause by clause, takes place. A chairman of standing committee, whose job is to consider the provisions, also has the power to amend it. When the committee stage is finished the Bill returns back to the House of Commons for its report stage where it can be debated and further amendments proposed. At this point, the standing committee reports the Bill back to the House to give the members an opportunity to make proposals for change to a Bill which has been examined during the previous stage. The members can suggest the amendments or the new clauses to the Bill and all the changes are voted upon. The report stage is immediately followed by the third reading which is the last chance to the members to vote on the contents of the Bill. During this stage the it is re-prese nted the House, where short debates may take place and a vote whether to accept or reject the legislation, but the questions relating to the general principles cannot be raised. When a Bill has passed through third reading in both Houses it is returned to the House where it started for the second Houses proposals for change to be considered. Both Houses must agree on the exact wording of the Bill. If one House refuses to make the changes proposed by the other the Bill might be re-introduced, but as Bills should be complete within one particular parliamentary Session, failure to reach the agreement might lead to the loss of the Bill. As legislation needs to be approved by both Houses we can seen that the House of Lords plays a vital role in lawmaking process. However, there are some exceptions when the two Houses cannot reach agreement, the Bill falls and the Commons use the Parliament Acts to pass the Bill without the consent of Lords. The Parliament Act of 1911 removed the House of Lords power to veto a Bill. Act also retained the House of Lords power to block any attempt to prolong the lifetime of a Parliament. The Parliament Act of 1911 limited the power of the Lords to delay the Bill more than for two years. The Parliament Act of 1949 reduced the Lords power to delay to one year, but the Parliament Act 1949 itself was introduced through the use of the Parliament Act of 1911. Though these procedures are used rarely as the House of Lords usually approve the legislature of the House of Commons, four substantive acts have been passed into law without the approval of the House of Lords, for example the controversial Hunting Act 2004, which was introduced to prohibit the hunting of mammals with dogs and was designed to outlaw the fox-hunti ng. It was passed despite the House of Lords opposition relying on the Parliament Act 1949. Another three acts passed without the consent of the Lords are The War Crimes Act 1991, The European Parliamentary Elections Act 1999, The Sexual Offences (Amendment) Act 2000. Since 1949 a Money Bill containing only financial provisions can be enacted without the House of Lords consent after the delay of one month. The last stage in the lawmaking process is the Royal Assent it is required before any Bill becomes a law.

The Purpose of the Federal Reserve System Essay -- The Fed and the Eco

Over the past few years we have realized the impact that the Federal Government has on our economy, yet we never knew enough about the subject to understand why. While taking this Economics course it has brought so many things to our attention, especially since we see inflation, gas prices, unemployment and interest rates on the rise. It has given us a better understanding of the effect of the Government on the economy, the stock market, the interest rates, etc. Since the Federal Government has such a control over our Economy, we decided to tackle the subject of the Federal Reserve System and try to get a better understanding of the history, the structure, and the monetary policy of the power that it holds. The Federal Reserve System is the central banking authority of the United States. It acts as a fiscal agent for the United States government and is custodian of the reserve accounts of commercial banks, makes loans to commercial banks, and is authorized to issue Federal Reserve notes that constitute the entire supply of paper currency of the country. Created by the Federal Reserve Act of 1913, it is comprised of 12 Federal Reserve banks, the Federal Open Market Committee, and the Federal Advisory Council, and since 1976, a Consumer Advisory Council which includes several thousand member banks. The board of Governors of the Federal Reserve System determines the reserve requirements of the member banks within statutory limits, reviews and determines the discount rates established pursuant to the Federal Reserve Act to serve the public interest; it is governed by a board of nine directors, six of whom are elected by the member banks and three of whom are appointed by the Board of Govern ors of the Federal Reserve System. The Federal Reserve banks are located in Boston, New York, Philadelphia, Chicago, San Francisco, Cleveland, Richmond, Atlanta, Saint Louis, Minneapolis, Kansas City and Dallas. The Federal Open Market Committee, consisting of the seven members of the Board of Governors and five members elected by the Federal Reserve banks, is responsible for the determination of Federal Reserve Bank policy in the purchase and sale of securities on the open market. The Federal Advisory Council, whose role is purely advisory, consists of 12 members if they meet membership qualifications. The Federal Reserve System exercises its regulatory powers in seve... ...erve. We feel that the latter is on the radical side of thinking, and that overall the Federal Reserve has the best interest of the nation and international economy in all their decisions regarding the increases in interest rates, etc. Since the onset of the Federal Reserve we have not gone into a major depression, and over a course of time there will be times when our economy will peak and boom and the Fed will feel that it is time to slow the economy by raising the rates. Bibliography FED 101 Hosted by The Federal Reserve Bank of Kansas City. http://www.kc.frb.org/fed101 Friedman, Milton and Jacobson Schwartz, Anna. A Monetary History of the United States, 1867-1960. Princeton, 1963 Hailstones, Thomas and Rothwell, John. Managerial Economics, 1993. Prentice Hall, 1993 Metzler, Allan H. A History of the Federal Reserve, Vol I and II. University Press Books, 2002 National Information Center for the Federal Reserve System. http://www.ffiec.gov/nic Rabboh, Bob and Bartson, Ronald J. Principles of Economics. Pearson, 2002 The Federal Reserve Board. http://www.federalreserve.gov The Federal Reserve System Online. http://www.federalreserveonline.org

The Toyota Marketing Strategy

[pic] Introduction 1. Introduction Navana Limited stands as the authorized distributor of Toyota cars in Bangladesh, so we have chosen them to make a successful marketing plan on Toyota cars. Our area of concentration was centered on the new model of Toyota Corolla-GLi. This is the latest car of Toyota Corolla that has been recently launched in Bangladesh by Navana Limited in November 2007 at Japan trade fair in Bangladesh. The brand name Corolla of Toyota is well known for producing cars for the common people but this car is an upgraded model of Corolla. [pic] Company Profile 2. Company Profile 2a. Company Overview Toyota Motor Corporation is a multinational corporation headquartered in Japan. Today, Toyota is the world's third largest manufacturer of automobiles. Providing the most reliable automobile for its customer is the Toyota’s specialty. Toyota Motor Corporation recently celebrated its 70 years both as a carmaker and half a century of selling cars in America. In 2007 Toyota sold 8. 52m vehicles and its net income rose by 20% and become $14 billion. Moreover Toyota is aiming to sell 10. 4m vehicles in 2009. In Bangladesh it is the most popular automobile company to the car user and it has almost 70% market share in our country. It is always interested to get the attention of the young generation, family people, working executives, service holders, business people, in one word all kind of people. â€Å"Its mission† is to predict consumer trends and create a lineup of cars and trucks to capitalize on them. Each professional is expected to spend time out in the field talking to car buyers. The Japanese have a name for it: genchi genbutsu – go to the scene and confirm the actual happenings. With Toyota, one thing has never changed that their commitment to the communities where they do business. Toyota spends over billions of billion on R, design, manufacturing, sales and marketing operations. Over the world they have sales /service offices, financial service offices, R centers, holding company, manufacturing facilities, design centers, Hino operation facilities, Supplier state etc. 2b. History Kiichiro Toyoda, founder of the toyota Motor Corporation, was born in 1894. His father Sakichi Toyoda became famous as he inventor of the automatic loom. Inheriting the spirit of research and creation from his father, Kiichiro devoted his entire life to the manufacturing of cars, which was an unknown frontier at that time. In 1933, Toyoda Automatic Loom Works created a new division devoted to the production of automobiles under the direction of the founder's son, Kiichiro Toyoda. Kiichiro Toyoda had traveled to Europe and the United States in 1929 to investigate automobile production. After years of hard work, he finally succeeded in completing the A1 prototype vehicle in 1935. That was the beginning of the history of the Toyota Motor Corporation. Toyoda Automatic Loom Works was encouraged to develop automobile production by the Japanese government and Model AA passenger car was the first production model of Toyota in 1936. [pic] Replica of the Toyota Model AA, the first production model of Toyota in 1936 Toyota Motor Co. was established as an independent and separate company in 1937. The company was founded by Kiichiro Toyoda as a spinoff from his father's company Toyota Industries to create automobiles. Toyota also owns and operates Lexus and Scion brands. Toyota is headquartered in Aichi, Nagoya and in Tokyo. In addition to manufacturing automobiles, Toyota provides financial services through its division Toyota Financial Services and also creates robots. 2c. Product Line of Toyota Toyota operates in Bangladesh through Navana Group, under Navana Limited. The product line of Toyota’s brand new cars, that are marketed by Navana Limited and are available in Bangladesh are: 1. TOYOTA Yaris 2. TOYOTA Corolla GLi 3. TOYOTA CAMRY 4. TOYOTA Avanza 5. TOYOTA Rav4 6. TOYOTA Fortuner 7. TOYOTA Prado 8. TOYOTA Land Cruiser 9. TOYOTA Hilux 10. TOYOTA Dyna 11. TOYOTA Hiace 12. TOYOTA Coaster [pic] Current marketing situation 3. Current marketing situation There is a huge market for automobile industry worldwide. In this global earth people need to communicate with others each and every minute. Transportation is one way that facilitates communication. The market demand for cars rise and fall time to time, but the demand never fell to the ground. The current market situation of cars is a little unstable for the fact that oil price has risen significantly worldwide that has resulted in a decrease of car sale worldwide. The same has also affected the Bangladeshi market. Different car dealers have reported that car sale has dropped significantly from last year, 2006-2007. There is also a rise in the car due to increase in cost of production. The steel price has risen significantly worldwide. Japan, Taiwan, importers of steel, are giving 27 to 30% more for buying steels. In Bangladesh, the government’s rules and regulation imposed on import, duty and tax has also caused the market of cars to decrease. [pic] Product Profile 4 . Product profile 4 a. Mission, Vision, Objectives & Goal Mission: The mission is to create a luxury vehicle that could go head to head with the world’s best automobiles. Vision: Setting new industry standards in operational excellence, market penetration, customer satisfaction and community commitment. Objective: Corolla GLi is clear in its objective to produce the segments most engaging driving dynamics while maintaining the brands traditional ride quality. Goal: From the outset, it is their goal to develop a luxury flagship vehicle that would be recognized as one of the finest cars in the world. 4 b. Products quality and features, design, packaging, brand name, extra services Brand name: Corolla GLi Features And Quality: ? Powerful performance: Responsive and quick to please, the Corolla effortlessly generates the power for driving pleasure, delivering subtly smooth and stable performance. ? Advanced technology: The Corolla generates outstanding power, minimizes its environmental impact, and provides warm reassurance. Wti technology: Based on driving conditions, it optimally changes the open/close timing of the intake valve, contributing to increased torque and output, better fuel economy and reduced Nitrogen oxides and hydrocarbon emissions. ? Crash safety body: It is comprised of a high integrity cabin with front and rear crumple zones that help absorb impact energy in a collision. ? Suspension: The Macpherson strut suspension on the front and torsion beam suspension on the rear were fine-tuned to provide excellent stability and control, and ride comfort. Keyless entry system: It lets to lock and unlock the doors from a distance. ? Moon roof: It incorporates one touch mode and a jam-protected system. ? Rear spoiler: The rear spoiler integrated into the trunk lid adds a sporty touch. ? Anti corrosion steel sheeting: The extensive use of anti corrosion steel sheeting protects the Corolla from rust, helping it to keep its goods looks for years to come. ? Immobiliser system: It provides security against theft. The car can only be started when the ID in the electronic matches the ID code in the engine immobiliser system. Fuel Level warning ? Wireless door lock ? Audio – AM/FM, CD Changer, 6 spk. ? Child protector ? Brake control valve – EBD Design ? Highly functional design: The ergonomics-based design of the instrument panel with its easy-to-use switches engages the driver, providing comfortable opera tion that enhances driving enjoyment. Convenient functional features and various integrated storage spaces enhance comfort ? Dynamic and advanced: With its dynamic and advanced design creating a high quality feeling, the Corolla continues winning hearts and minds right around the world. Sophisticated presence: First impressions are compelling. The short-nose, long-deck proportions highlight the advanced sedan styling. Together with its expensive cabin space, it exudes a distinctive presence. ? Generous appearance: The captivating design creates a feeling of great possibility. The wide tread and generous appearance set the stage for the spacious cabin. ? Refined interior details: The Corolla’s attention to details includes the distinctive curved design of the center console, the use of colors and textures, and the quality finish. Brakes: Disc brakes on all four wheels, ventilated on the front, are standard for all grades, giving sure stopping performance. ? Windshield Glass â €“ Green Laminated ? Outside rear view mirror ? Color Oxygen Sensor ? Head Rest – Front & Rear ? Rear Armrest – with Cup holder ? Inside Rear view mirror – Day & Night Colors available in Bangladesh ? Super White 2 ? Silver Metallic ? Blue Metallic ? Turquoise Mica Metallic ? Red Mica Metallic ? Grey Metallic ? Black Mica Packaging: It creates a spacious, comfortable cabin with excellent headroom, together with ample trunk space. Engine: The compact, lightweight engine integrates sophisticated technologies, which contribute to its excellent performance and low fuel consumption. Extra Service ? Immobiliser system: It provides security against theft. The car can only be started when the ID in the electronic matches the ID code in the engine immobiliser system. ? Keyless entry system: It lets to lock and unlock the doors from a distance. ? CD changer 4 c. Products position in the market compare to other product of the company with BCG growth matrix Boston Consulting groups (BCG)’s growth share matrix is a table that gives an idea about about market growth rate compare to relative market share. The market growth rate on the vertical axis indicates the growth rate of the market in which the business operates. And the relative market share on the horizontal axis indicates the market share compare to the other segments. It serves as a measure of the company’s strength in that market segment For BCG growth matrix, we have selected four models of Toyota Cars to analyze GLi’s position in market compare to other models. Models are- 1. Corolla GLi 2. Probox 3. Yaris 4. Crown | |Relative Market Share | | | |High Low | | | | | |Market High | |Growth | |Rate | | | |Low | HighLow High Figure: BCG Growth Matrix Our analysis on Corolla GLi compare to others is described below- Star: According to our observation, Probox falls into the position of Stars in the matrix table. Recently, Probox has reached at peak point in terms of selling. That is why their market growth rate is very high as well as market share. From the Bangladesh perspective, the demand of this car has increased so the company is trying to hold this position Question Mark: Corolla GLi falls under the category of this position. Because it is totally a new brand in Bangladesh, but has got very rapid sale within a short period of time. Therefore, their market growth rate is in the high position. On the other hand, as a new brand market share is not so high till now. Cash Cow: When market growth rate is low along with high market share then the product fall under this category. From our point of view, Yaris falls in to this position. Because present market growth rate of Yaris is not that much high compare to other though their market share is high. Dogs: In this position, both the market growth rate and market share is low. According to our observation, Crown falls into Dogs position in the matrix table. This is the model, which has less demand in Bangladesh that is why their market share is also low. 4 d. Market segmentation process Market segments are large identifiable groups within a market. There are four basic bases for segmenting consumer market. These variables can be used singly or in combination. These are- 1. Geographic segmentation 2. Demographic segmentation 3. Behavioral segmentation 4. Psychographic segmentation Now, considering Corolla GLi, we find that they also segment their market into groups based on the above segmentations. For this segmentation process, firstly they study the market and customers demand. They complete this process by analyzing the competitors’ products, segmentation as well as customers demand. The process is described below- Geographic segmentation: It is the process of dividing the market into different geographical units, such as country, city, nation, state, region etc. The company can operate in one or few geographic areas, or operate in all but pay attention to local variations. From Corolla GLi’s point of view that they segment their market based on – †¢ Country: In order to cover the whole world’s market they launch their product in different countries. To do so, in 2007 they first launch this model in Bangladesh. City: After selecting the country, they target those cities where they find more customer demands and wants. They actually select the cities after analyzing the purchasing power, living standard and so on. Demographic Segmentation: In this segmentation the market is divided in to groups on the basis of variables such as age, family size, life cycle, gender, income, occupation, education etc. These variables are the most popular bases for distinguishing customer groups. From corolla GLi point of view, they segment their market depending on income and occupation mostly and others have less affect in this segmentation part. As we know that they firstly go for market study to know customers demand as well as their purchasing power. For this purpose, they target those customers who have high income as well as in top position in their occupation to match whether they can afford this car or not. Behavioral segmentation: In this segmentation buyers are divided in to groups on the basis of their knowledge, attitude toward the product, use of, or response to a product. The behavioral variables are occasions, benefit, user status etc. If we look at the Corolla GLi’s segmentation process, we can see that they mainly focus on benefit variables and customers attitude toward the products. In benefit variables consumers actually look for products quality, services, economy, and speed. Therefore, corolla GLi is providing high quality, extra ordinary services along with high economic value to meet the customer demands. Moreover some customer’s attitude is to prefer branded products. They are basically quality concern people not price sensitive. Psychographics segmentation: In this segmentation the market is divided in to groups on the basis of life style, personality and social class. As we have mentioned earlier that GLi is a branded product targeting the upper class people so social class, life style, and personality play an important role in this segmentation. The people who are in the upper class and lead a luxurious life style they want such type of car that represent their status, image and pride in the society. Here corolla GLi holds all the characteristics that make satisfy these groups of customers. In addition, the customers who are ambitious, outgoing, demanding, compulsive and want to show a unique image may also buy this car as a symbol of attractiveness. Thus these four basic parts of segmentation process helps them to identify the proper customer demands and market. 4 e. Target market selection process After the segmentation process marketers identify one or more selected areas to enter into the market, this is known as target market selection process. There are different patterns of target market selecting. These are- 1. Single segment concentration: Producing one product for one selected market. 2. Selective specialization: Offering different product for different market. Here, one sector can be covered by other. 3. Product/service specialization: Offering one product for all groups of people in order to minimize cost. 4. Market specialization: Offering different product for one selected market. 5. Full market coverage: Marketers try to cover full market by offering different products for different market. After analyzing the five patterns of target market selection, we can say that Corolla GLi follows the Single segment concentration. Because- ? They don’t have any other sub model of GLi. It indicates that they are producing only one product. ? Also they are producing this product targeting only one group of people, which are the upper class people. From Corolla GLi point of view, they select their target market by considering the customer’s demand like- what feature, design, and benefit they want. Last of all, they try to match these with the customer ability and purchasing power. As it is mentioned earlier that they are following single segment concentration so the benefits for selecting this pattern are mentioned below- ? Through the Single segment concentration, marketers gain a strong knowledge of the segments need and achieve a strong market presence. ? With the help of Single segment concentration they can increase their sale, which can earn a high return on its investment. 4 f. Types of Consumer behavior Buying Behavior is the decision processes and acts of people involved in buying and using products. There are four typical types of buying behavior based on the type of products that intends to be purchased. These are- Complex buying behavior: It is a buying behavior where the individual purchases a high value brand and seeks a lot of information before the purchase is made. In this process, buyer first develops belief about the product then develops attitude about the product and lastly makes a thoughtful choice. Variety-seeking buying behavior: It is a buying behavior where the individual likes to shop around and experiment with different products. Here brand switching occurs for the sake of variety rather than dissatisfaction and look for cheaper price. Dissonance-reducing buying behavior: It is a buying behavior when buyer is highly involved with the purchase of the product. There exists little difference between existing brands, so customers become confused. Habitual buying behavior: It is a buying behavior where the individual buys a product out of habit e. g. a daily newspaper, sugar or salt etc. After analyzing the above point it is quite clear that Corolla GLi car buyers are following complex buying behavior, because they are highly involved in purchase and aware of significant difference among brands. We know that this car is expensive, risky and self- expressive so buyer buy infrequently. Furthermore, this type of customers buy car by differentiating the products with other significant brands like- Mercedes, BMW. Here, Corolla marketers also compare their product with BMW, Mercedes. Mainly, customers are concern about brand not price so they look for brand’s benefits and quality, which will show the symbol of pride, status in the society. 4 g. Steps in the consumer buying behavior Consumer Buying Behavior: It refers to the buying behavior of final consumers- individual and households, who buy goods and services for personal consumption. There are five steps by which consumer buying behavior pass through- Fig: Steps of consumer buying behavior Likewise, to buy Corolla GLi consumers may through all the steps. These are explained below- Need Recognition: In this step a consumer become aware of a problem or need. As we have mentioned earlier that Corolla GLi is a car of status, reputation, image and so on. When people reach that level where they feel to have such a prestigious car, they are in the need recognition stage. So they want such a brand new car, which will higher up their position in the society as well as match with their societal status. Information Search: When customers become aware of the need, they go for information search. They can collect information from various sources, such as personal, commercial, public sources etc. In personal sources, they can collect reliable information from their friends and others who have Corolla GLi or may know well about this car. ? They also can go for visiting Toyota show rooms in order to collect more accurate information, which refers as commercial sources. ? Print & elect ronic media, advertisement, billboard, Internet etc can also act as public sources in order to provide information to customers. Evaluation of Alternatives: In this stage, the consumers form preferences among the brands in the choice set. After completing the information search stage, customers look for competitive brand information by which they can evaluate the brands with each others. Here customers also evaluate Corolla GLi with other brand new cars and try to find out significant differences among them. They compare the brand image, features, services, speed, design, and other facilities and benefits among the alternatives. Purchase Decision: After completing the evaluation process, the select the most preferred brand which is suitable for them and then they decide to buy the product. In the case of Corolla Gli, after evaluating all the alternatives the pick Corolla GLi as it is fitted from all perspective. Attitudes of others who already have Corolla GLi, plays an important role to take the purchase decision. And then go for final consumption. Post-purchase Behavior After purchasing the product, consumers will experience some level of satisfaction or dissatisfaction. In the case of Corolla Gli, consumer may try to figure out their satisfaction level. Whether the car’s perceived performance is satisfactory or not. 4 h. Product Life cycle stage determination [pic] Corolla GLi was launched in November 2007 in Bangladesh it went through the introduction stage with great success and now it is in the growth stage the features, quality and brand name of the car are attracting more and more potential buyers day by day. 4 i. SWoT analysis SWOT stands for internal Strengths and Weaknesses and external Opportunities and Threats. It is used to gauge the degree of â€Å"fit† between the organizations’s strategies and its product and to suggest ways in which the organization can profit from strengths and opportunities and shield itself against weaknesses and threats. [pic] Strengths ? Brand new product ? It represents luxurious life style and symbol of status. ? Showing reliability by the company name Toyota. ? Using WT-i technology Weakness ? Since it is one of the models of corolla so some people may have misperception about GLi as a new brand. ? Because of the mentioned reason also GLi still don’t have own Brand image. ? No product line and variation in model. Opportunities ? Offering product, which is equivalent to other luxuries car. ? Attracting new customer by providing quality product. Threat Entrance of new competitors. ? Government regulations (new or revised). [pic] Pricing for Corolla Gli 5. Pricing for Corolla Gli 5a. Price A firm sets prices when it develops a new product, whe n it introduces its regular product into a new distribution channel or geographical area, when it adds new features in the product, etc. Price is the only element in the marketing mix that generates revenue the other element generates cost. Price is considered as the major determinant of buyer choice especially in the poorer nation and with commodity type products. Companies set their prices in different ways based on cost, value, competitors, customers, etc. Each pricing strategy is different from the. Cost based pricing strategy is where the organization set prices based on cost of production with that amount a certain markup is added for the profit and the product is sold. Competitors based pricing strategy depends on the price of the competitors what they would charge for the product for this pricing strategy the organization either charges same or low price than the competitors. 5b. Pricing strategy of Toyota Corolla Gli Toyota mainly follows cost based pricing strategy for the entire car it manufactures for the luxurious car it follows both cost based pricing strategy and value based pricing strategy. They deliver the value promised by their value proposition and the customer perceives the value. To communicate and enhance perceived value in buyers mind Toyota uses other marketing mix elements such as advertising and sales force. Value based pricing depends on the product performance, quality, features, customer service, etc. For Corolla GLi Toyota uses both cost based and value based pricing strategy as this is one of the most luxurious cars of Toyota. Navana is the only importer in Bangladesh who buys Corolla GLi from Toyota. Initially when the car was launched it was sold at a price of 1950000 taka but now as duty fee has increased and international currency fluctuated the price of Corolla GLi is now 2250000 taka. For the pricing of this car Toyota is also following other pricing strategies they are price skimming strategy which is they are charging maximum price as it is a new product, the demand of this car is already present in other countries and the buyers are also willing to pay any price to buy this car. It is following premium pricing which is charging high price for the high quality car . It is also following the optional product pricing e. g. for with the car Toyota is providing a luxorious comfortable interior with leather seats, cd player, etc. Therefore Final price is determined with all these strategies plus the cost of import, duty fee, the cost of shipment and the markup of Navana. pic] Distribution for Corolla Gli 6. Distribution for Corolla Gli 6a. Distribution or location strategy Most producers do not sell their goods directly to final consumers they use channels or marketing intermediaries to deliver their product to the ultimate consumers. By using intermediaries the cost of the producers and their number of transaction decreases. 6b. Channel dynamics †¢ Conventional marketing system- manufacturer, wholesaler, retailer work as independent system. No one has control over the other. Each member of the channel has separate objectives. †¢ Vertical marketing system- all the members of the channel work as a unified team. Hybrid marketing system- when the product is sold by using more than one channel 6c. Distribution of Toyota Toyota has distributors in almost every country. In Bangladesh the main distributor of Toyota is Navana. Navana performs many functions of Toyota. They gather information about potential and current customers of Bangladesh about the government policy and other external factors and communicate the information to Toyota. They make people of Bangladesh aware of the new cars their features and benefits e. g. to promote Corolla Gli Navana used print media, internet, etc for advertisement. They communicate with the customers dir ectly and sell the cars. As Toyota uses Just-in-time approach to some extent they depend on their distributors as the distributors provide them information about customers demand or about the cars of the competitors and Toyota produce their cars accordingly. Toyota and Navana together follows the Vertical marketing system where they work as a unified team. If Toyota wants to launch a new car in Bangladesh they provide Navana with all the information about the car Navana then analyzes the current marketing situation about the competitors and orders as per demand which is then delivered after 5months through shipment. Navana is an exclusive distributor of Toyota they are given full authority to sell the cars of Toyota. [pic] Promotional tools 7. Promotional tools Every company has to sell their products to their desire customers. For that they need to communicate with them. In this circumstances every company use some promotional tools to sell their product. As Toyota selling specialty product GLI car, they are also using some promotional tools to capture more and more market share. 7 a. Objective of promotional activity Toyota has some certain objectives behind their promotional activities. Those ares- ? Giving information about the product ? What’s new in features and benefits ? Trying to create brand value of GLI ? Ultimate increase of market share 7 b. Promotional tools of corolla GLI Toyota using three basic promotional tools to promote Corolla GLI. ? Advertising ? Personal selling ? Direct marketing Advertising Advertising is the paid form of non-personal presentation by an individual organization to promote their products towards their customers. Toyota gives advertisement of their product through different media to promote their products towards their customers. Toyota using paper and bill board for their advertising. They go for billboards which are situated in Bijoy Shoroni, Manik Mia Avenue, Kamal Ataturk Avenue, Gulshan 1 & 2, infront of Shonargoan Hotel, Dhanmondi 27, Newmarket. In Chittagong – Newmarket, Port city, Nasira bad and Kulshi etc. Personal selling Toyota using personal selling tools to sell and promote corolla GLI. Personal selling is the direct way to connect with customers. Toyota first introduce GLI in Japan trade fair, it’s a way of personal selling. Also Under personal selling they go for corporate selling and they target bank and company high ranked personalities to buy their product. It’s a very effective form of selling corolla GLI. Direct marketing Direct marketing is another tool that used by Toyota to aware about GLI to their customers. Direct marketing is way of marketing where, there are no physical contacts with the customers. They did E-mail campaign to promote GLI as direct marketing. 7 c. Media used by Toyota As Toyota wants to sell their product GLI, they use some media to provide their message to their desired customers. Toyota uses both personal and nonpersonal communication channels to promote GLI. ? Personal communication channels Personal communication channels involve two or more person communicating directly with each other face to face, person to audience, over the phone or through mail, where company get the opportunity to receive feedback from customers etc. To promote GLI Toyota uses face to face, person to audience and mail as personal communication channels. Also word of mouth behavior acting as personal communication channel. ? Nonpersonal communication channels Nonpersonal communication include media, atmosphere and event, where no face to face communication occur. Moreover no opportunity to get feedback from the customers. Toyota uses print media, bill boards, car show etc as nonpersonal communication channel. 7 d. Media budget One of the most difficult marketing decision is determining how much to spend on promotion. There are some common methods of determining media budget. Those are affordable method, percentage on sales method, competitor’s parity method and objective and task method. From these Toyota is using a combine approach of affordable and objective-task method. But before that they are estimating the budget depending on product life, quantity and brand value. For GLI, Navana the authorized distributor of Toyota budgeted 20-30 lakh for the current year. 7 e. Advertisement effect on sales Toyota marked GLI as a successful project in Bangladesh. To become successful Toyota is doing a lot of promotional activities. They also found positive effect on their sales from their promotional activities. As a result they able to sell 300 to 350 Gli car within 8 months. It’s a great achievement in term of selling luxury sedan. Toyota is very successful in term of their promotional activities. Also they use different types of promotional tools to become successful in Bangladeshi competitive car selling market. [pic] Problem Identification Car is marked as specialty product and also perceived as luxurious product in our country. So it’s a bit difficult to maintain a luxurious product like Toyota GLI in every segment of marketing. Although it’s a very successful project of Toyota in Bangladesh but they faced some problems. 1. Perceived value of corolla in customers mind Customers of Bangladesh perceived that corolla is a brand of common people. As GLI is a sedan of corolla segment, customers perceived that it’s not a high branded car. Although it is a corolla segment car but it is a high grade car of corolla then other corolla cars. As customers think it is a common brand car they don’t want to buy it on that amount of value. So it’s become a huge marketing problem for corolla GLI. 2. Brand name GLI Basically GLI doesn’t have any meaning. But customers want to know the meaning of it. So it creates some sort of problem to give the proper answer of meaning of GLI. 3. High price GLI is a car of high grade, so it’s a high price car. As more people wants to buy affordable car they don’t want to buy it at a high price. Also some don’t want to buy a corolla branded product at a high value. So the high price of the car creates some sort of problem. 4. Off stock delivery time Toyota uses Just in time inventory system. So they manufacture product only on demand. If the stock of GLI car comes to an end then it needs 120 day to delivery the product again through shipment. So off stock delivery time is a problem of Toyota for any car as well for GLI. 5. Rapid growth of competitors high branded cars Previously, the Bangladeshi car market was captured by Toyota. But in term of luxurious and high branded car, now Nissan, Honda and Mitsubishi entered the market with a great deal. So market becomes competitive and it’s a new problem for Toyota in Bangladeshi market. 6. Import of recondition cars Huge amount of recondition cars are importing from Japan to our country. So the new branded cars are loosing their appeal in the market. 7. Unstable car import and duty law and regulation Car import and duty law is very unstable in our country. It creates hazard for the company to do their business smoothly. Toyota is facing some problems regarding GLI. They are also trying their best to solve those problems. Moreover they marked these problems positively and from the GLI experience they will able to avoid these hazards for their up coming projects. 9. Recommendations 1. Customers perceived value- To overcome this situation marketers need to increase the brand value of Corolla GLi. They can increase brand value by adding more features than other Corolla cars, or even compared to the competitors same level cars. They can utilize the brand equity of Toyota cars that prevails in the market. They can highlight the brand GLi besides Toyota Corolla. They can differentiate GLi from other Corolla. They can differentiate GLi from other Corolla line extensions by highlighting the existing features. They can introduce new designs in terms of color, body kits etc; new features and also extra facilities. 2. High price- As the price of Corolla GLi is high; to overcome this situation marketers can add more value to the product rather than cutting the price. They can have value addition to the product- a. perceived value in terms of brand image. b. tangible value- marketers can introduce new features and design by producing new colors, body kits etc. They can avail more extra facilities and benefits in the car. 3. Though the management philosophy of Toyota that is the Just-in- time approach is not a current problem but rather is referred as a potential problem in the long run. Our recommendation would be to study and be informed about the market demand all the time to avoid any situation of being out of stock. 4. The rapid growth of competitors branded cars is a great threat to Toyota worldwide as well as in Bangladesh. The marketer should always be aware of bringing in, what are the benefits that will be available etc and plan accordingly to reduce the threat of being out of model or even out of market. References & Bibliography www. amartoyota. com www. toyota. com www. toyotahistory. com www. toyotacarzone. com Marketing Management-Philip Kotler 11th edition, Prentice Hall Advertising Principle & Practice – William Wells and Sandra Moriarty, 7th edition, Prentice Hall. www. bdnewspaper. com ———————————————- ———————– Star (Probox) Question Mark (Corolla GLi) Cash Cow (Yaris) Dogs (Crown) H igh Low Involvement Involvement Significant difference Between brands Few difference Between brands Complex Buying Variety Seeking buying Habitual buying Dissonance Reducing Buying Purchase Decision Post-purchase Behavior Evaluation of Alternatives Information Search Need Recognition Time Product Develop- ment Introduction Profits Sales Growths Maturity Decline Losses/ Investments ($) Sales and Profits ($) GLi

Lacsap’s Fractions

Lacsap’s Fractions IB Math 20 Portfolio By: Lorenzo Ravani Lacsap’s Fractions Lacsap is backward for Pascal. If we use Pascal’s triangle we can identify patterns in Lacsap’s fractions. The goal of this portfolio is to ? nd an equation that describes the pattern presented in Lacsap’s fraction. This equation must determine the numerator and the denominator for every row possible. Numerator Elements of the Pascal’s triangle form multiple horizontal rows (n) and diagonal rows (r). The elements of the ? rst diagonal row (r = 1) are a linear function of the row number n. For every other row, each element is a parabolic function of n.Where r represents the element number and n represents the row number. The row numbers that represents the same sets of numbers as the numerators in Lacsap’s triangle, are the second row (r = 2) and the seventh row (r = 7). These rows are respectively the third element in the triangle, and equal to each other bec ause the triangle is symmetrical. In this portfolio we will formulate an equation for only these two rows to ? nd Lacsap’s pattern. The equation for the numerator of the second and seventh row can be represented by the equation: (1/2)n * (n+1) = Nn (r) When n represents the row number.And Nn(r) represents the numerator Therefore the numerator of the sixth row is Nn(r) = (1/2)n * (n+1) Nn(r) = (1/2)6 * (6+1) Nn(r) = (3) * (7) Nn(r) = 21 Figure 2: Lacsap’s fractions. The numbers that are underlined are the numerators. Which are the same as the elements in the second and seventh row of Pascal’s triangle. Figure 1: Pascal’s triangle. The circled sets of numbers are the same as the numerators in Lacsap’s fractions. Graphical Representation The plot of the pattern represents the relationship between numerator and row number. The graph goes up to the ninth row.The rows are represented on the x-axis, and the numerator on the y-axis. The plot forms a parabo lic curve, representing an exponential increase of the numerator compared to the row number. Let Nn be the numerator of the interior fraction of the nth row. The graph takes the shape of a parabola. The graph is parabolical and the equation is in the form: Nn = an2 + bn + c The parabola passes through the points (0,0) (1,1) and (5,15) At (0,0): 0 = 0 + 0 + c ! ! At (1,1): 1 = a + b ! ! ! At (5,15): 15 = 25a + 5b ! ! ! 15 = 25a + 5(1 – a) ! 15 = 25a + 5 – 5a ! 15 = 20a + 5 ! 10 = 20a! ! ! ! ! ! ! therefore c = 0 therefore b = 1 – a Check with other row numbers At (2,3): 3 = (1/2)n * (n+1) ! (1/2)(2) * (2+1) ! (1) * (3) ! N3 = (3) therefore a = (1/2) Hence b = (1/2) as well The equation for this graph therefore is Nn = (1/2)n2 + (1/2)n ! which simpli? es into ! Nn = (1/2)n * (n+1) Denominator The difference between the numerator and the denominator of the same fraction will be the difference between the denominator of the current fraction and the previous fraction . Ex. If you take (6/4) the difference is 2. Therefore the difference between the previous denominator of (3/2) and (6/4) is 2. ! Figure 3: Lacsap’s fractions showing differences between denominators Therefore the general statement for ? nding the denominator of the (r+1)th element in the nth row is: Dn (r) = (1/2)n * (n+1) – r ( n – r ) Where n represents the row number, r represents the the element number and Dn (r) represents the denominator. Let us use the formula we have obtained to ?nd the interior fractions in the 6th row. Finding the 6th row – First denominator ! ! ! ! ! ! ! ! ! ! ! ! – Second denominator ! ! ! ! ! ! ! ! ! ! ! ! ! denominator = 6 ( 6/2 + 1/2 ) – 1 ( 6 – 1 ) ! = 6 ( 3. 5 ) – 1 ( 5 ) ! 21 – 5 = 16 denominator = 6 ( 6/2 + 1/2 ) – 2 ( 6 – 2 ) ! = 6 ( 3. 5 ) – 2 ( 4 ) ! = 21 – 8 = 13 ! ! -Third denominator ! ! ! ! ! ! ! ! ! ! ! ! – Fourth denominator ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! – Fifth denominator ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! denominator = 6 ( 6/2 + 1/2 ) – 3 ( 6 – 3 ) ! = 6 ( 3. 5 ) – 3 ( 3 ) ! = 21 – 9 = 12 denominator = 6 ( 6/2 + 1/2 ) – 2 ( 6 – 2 ) ! = 6 ( 3. 5 ) – 2 ( 4 ) ! = 21 – 8 = 13 denominator = 6 ( 6/2 + 1/2 ) – 1 ( 6 – 1 ) ! = 6 ( 3. 5 ) – 1 ( 5 ) ! = 21 – 5 = 16 ! ! We already know from the previous investigation that the numerator is 21 for all interior fractions of the sixth row.Using these patterns, the elements of the 6th row are 1! (21/16)! (21/13)! (21/12)! (21/13)! (21/16)! 1 Finding the 7th row – First denominator ! ! ! ! ! ! ! ! ! ! ! ! – Second denominator ! ! ! ! ! ! ! ! ! ! ! ! – Third denominator ! ! ! ! ! ! ! ! ! ! ! ! – Fourth denominator ! ! ! ! ! ! ! ! ! ! ! ! ! ! denominator = 7 ( 7/2 + 1/2 ) – 1 ( 7 – 1 ) ! =7(4)–1(6) ! = 28 – 6 = 22 denominator = 7 ( 7/2 + 1/2 ) – 2 ( 7 – 2 ) ! =7(4)–2(5) ! = 28 – 10 = 18 denominator = 7 ( 7/2 + 1/2 ) – 3 ( 7 – 3 ) ! =7(4)–3(4) ! = 28 – 12 = 16 denominator = 7 ( 7/2 + 1/2 ) – 4 ( 7 – 3 ) ! =7(4)–3(4) ! = 28 – 12 = 16 ! ! ! ! ! ! Fifth denominator ! ! ! ! ! ! ! ! ! ! ! ! – Sixth denominator ! ! ! ! ! ! ! ! ! ! ! ! denominator = 7 ( 7/2 + 1/2 ) – 2 ( 7 – 2 ) ! ! =7(4)–2(5) ! ! = 28 – 10 = 18 ! ! denominator = 7 ( 7/2 + 1/2 ) – 1 ( 7 – 1 ) ! =7(4)–1(6) ! = 28 – 6 = 22 We already know from the previous investigation that the numerator is 28 for all interior fractions of the seventh row. Using these patterns, the elements of the 7th row are 1 (28/22) (28/18) (28/16) (28/16) (28/18) (28/22) 1 General Statement To ? nd a general statement we combined the two equations needed to ? nd the numerator and to ? nd the denominator. Which are (1/2)n * (n+1) to ? d the numerator and (1/2)n * (n+1) – n( r – n) to ? nd the denominator. By letting En(r) be the ( r + 1 )th element in the nth row, the general statement is: En(r) = {[ (1/2)n * (n+1) ] / [ (1/2)n * (n+1) – r( n – r) ]} Where n represents the row number and r represents the the element number. Limitations The ‘1’ at the beginning and end of each row is taken out before making calculations. Therefore the second element in each equation is now regarded as the ? rst element. Secondly, the r in the general statement should be greater than 0. Thirdly the very ? rst row of the given pattern is counted as the 1st row.Lacsap’s triangle is symmetrical like Pascal’s, therefore the elements on the left side of the line of symmetry are the same as the elements on the right side of the line of symmetry, as shown in Figure 4. Fourthly, we only formulated equations based on the second and the seventh rows in Pascal’s triangle. These rows are the only ones that have the same pattern as Lacsap’s fractions. Every other row creates either a linear equation or a different parabolic equation which doesn’t match Lacsap’s pattern. Lastly, all fractions should be kept when reduced; provided that no fractions common to the numerator and the denominator are to be cancelled. ex. 6/4 cannot be reduced to 3/2 ) Figure 4: The triangle has the same fractions on both sides. The only fractions that occur only once are the ones crossed by this line of symmetry. 1 Validity With this statement you can ? nd any fraction is Lacsap’s pattern and to prove this I will use this equation to ? nd the elements of the 9th row. The subscript represents the 9th row, and the number in parentheses represents the element number. – E9(1)!! ! – First element! ! ! ! ! ! ! ! ! ! ! ! ! – E9(2)!! ! – Second element! ! ! ! ! ! ! ! ! ! ! ! ! – E9(3)!! ! – Third element! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! {[ n( n/2 + 1/2 ) ] / [ n( n/2 + 1/2 ) – r( n – r) ]} {[ 9( 9/2 + 1/2 ) ] / [ 9( 9/2 + 1/2 ) – 1( 9 – 1) ]} {[ 9( 5 ) ] / [ 9( 5 ) – 1( 8 ) ]} {[ 45 ] / [ 45 – 8 ]} {[ 45 ] / [ 37 ]} 45/37 {[ n( n/2 + 1/2 ) ] / [ n( n/2 + 1/2 ) – r( n – r) ]} {[ 9( 9/2 + 1/2 ) ] / [ 9( 9/2 + 1/2 ) – 2( 9 – 2) ]} {[ 9( 5 ) ] / [ 9( 5 ) – 2 ( 7 ) ]} {[ 45 ] / [ 45 – 14 ]} {[ 45 ] / [ 31 ]} 45/31 {[ n( n/2 + 1/2 ) ] / [ n( n/2 + 1/2 ) – r( n – r) ]} {[ 9( 9/2 + 1/2 ) ] / [ 9( 9/2 + 1/2 ) – 3 ( 9 – 3) ]} {[ 9( 5 ) ] / [ 9( 5 ) – 3( 6 ) ]} {[ 45 ] / [ 45 – 18 ]} {[ 45 ] / [ 27 ]} 45/27 E9(4)!! ! – Fourth element! ! ! ! ! ! ! ! ! ! ! ! ! – E9(4)!! ! – Fifth element! ! ! ! ! ! ! ! ! ! ! ! ! – E9(3)!! ! – Sixth element! ! ! ! ! ! ! ! ! ! ! ! ! – E9(2)!! ! – Seventh element! ! ! ! ! ! ! ! ! ! ! ! ! â₠¬â€œ E9(1)!! ! – Eighth element! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! [ n( n/2 + 1/2 ) ] / [ n( n/2 + 1/2 ) – r( n – r) ]} {[ 9( 9/2 + 1/2 ) ] / [ 9( 9/2 + 1/2 ) – 4( 9 – 4) ]} {[ 9( 5 ) ] / [ 9( 5 ) – 4( 5 ) ]} {[ 45 ] / [ 45 – 20 ]} {[ 45 ] / [ 25 ]} 45/25 {[ n( n/2 + 1/2 ) ] / [ n( n/2 + 1/2 ) – r( n – r) ]} {[ 9( 9/2 + 1/2 ) ] / [ 9( 9/2 + 1/2 ) – 4( 9 – 4) ]} {[ 9( 5 ) ] / [ 9( 5 ) – 4( 5 ) ]} {[ 45 ] / [ 45 – 20 ]} {[ 45 ] / [ 25 ]} 45/25 {[ n( n/2 + 1/2 ) ] / [ n( n/2 + 1/2 ) – r( n – r) ]} {[ 9( 9/2 + 1/2 ) ] / [ 9( 9/2 + 1/2 ) – 3 ( 9 – 3) ]} {[ 9( 5 ) ] / [ 9( 5 ) – 3( 6 ) ]} {[ 45 ] / [ 45 – 18 ]} {[ 45 ] / [ 27 ]} 45/27 {[ n( n/2 + 1/2 ) ] / [ n( n/2 + 1/2 ) – r( n – r) ]} {[ 9( 9/2 + 1/2 ) ] / [ 9( 9/2 + 1/2 ) – 2( 9 – 2) ]} {[ 9( 5 ) ] / [ 9( 5 ) – 2 ( 7 ) ] } {[ 45 ] / [ 45 – 14 ]} {[ 45 ] / [ 31 ]} 45/31 {[ n( n/2 + 1/2 ) ] / [ n( n/2 + 1/2 ) – r( n – r) ]} {[ 9( 9/2 + 1/2 ) ] / [ 9( 9/2 + 1/2 ) – 1( 9 – 1) ]} {[ 9( 5 ) ] / [ 9( 5 ) – 1( 8 ) ]} {[ 45 ] / [ 45 – 8 ]} {[ 45 ] / [ 37 ]} 45/37 From these calculations, derived from the general statement the 9th row is 1 (45/37)! ! (45/31)! ! (45/27)! (45/25)! (45/25)! (45/27) (45/31)! (45/37)! ! 1 Using the general statement we have obtained from Pascal’s triangle, and following the limitations stated, we will be able to produce the elements of any given row in Lacsap’s pattern. This equation determines the numerator and the denominator for every row possible.