False position method and bisection

False position method and bisection In numerical analysis, the false position method or regula falsi method is a root-finding algorithm that combines features from the bisection method and the secant method. The method: The first two iterations of the false position method. The red curve shows the function f and the blue lines are the secants. Like the bisection method, the false position method starts with two points a0 and b0 such that f(a0) and f(b0) are of opposite signs, which implies by the intermediate value theorem that the function f has a root in the interval [a0, b0], assuming continuity of the function f. The method proceeds by producing a sequence of shrinking intervals [ak, bk] that all contain a root of f. At iteration number k, the number is computed. As explained below, ck is the root of the secant line through (ak, f(ak)) and (bk, f(bk)). If f(ak) and f(ck) have the same sign, then we set ak+1 = ck and bk+1 = bk, otherwise we set ak+1 = ak and bk+1 = ck. This process is repeated until the root is approximated sufficiently well. The above formula is also used in the secant method, but the secant method always retains the last two computed points, while the false position method retains two points which certainly bracket a root. On the other hand, the only difference between the false position method and the bisection method is that the latter uses ck = (ak + bk) / 2. Bisection method In mathematics, the bisection method is a root-finding algorithm which repeatedly bisects an interval then selects a subinterval in which a root must lie for further processing. It is a very simple and robust method, but it is also relatively slow. The method is applicable when we wish to solve the equation for the scalar variable x, where f is a continuous function. The bisection method requires two initial points a and b such that f(a) and f(b) have opposite signs. This is called a bracket of a root, for by the intermediate value theorem the continuous function f must have at least one root in the interval (a, b). The method now divides the interval in two by computing the midpoint c = (a+b) / 2 of the interval. Unless c is itself a rootwhich is very unlikely, but possiblethere are now two possibilities: either f(a) and f(c) have opposite signs and bracket a root, or f(c) and f(b) have opposite signs and bracket a root. We select the subinterval that is a bracket, and apply the same bisection step to it. In this way the interval that might contain a zero of f is reduced in width by 50% at each step. We continue until we have a bracket sufficiently small for our purposes. This is similar to the computer science Binary Search, where the range of possible solutions is halved each iteration. Explicitly, if f(a) f(c) Advantages and drawbacks of the bisection method Advantages of Bisection Method The bisection method is always convergent. Since the method brackets the root, the method is guaranteed to converge. As iterations are conducted, the interval gets halved. So one can guarantee the decrease in the error in the solution of the equation. Drawbacks of Bisection Method The convergence of bisection method is slow as it is simply based on halving the interval. If one of the initial guesses is closer to the root, it will take larger number of iterations to reach the root. If a function is such that it just touches the x-axis (Figure 3.8) such as it will be unable to find the lower guess, , and upper guess, , such that For functions where there is a singularity and it reverses sign at the singularity, bisection method may converge on the singularity (Figure 3.9). An example include and, are valid initial guesses which satisfy . However, the function is not continuous and the theorem that a root exists is also not applicable. Figure.3.8. Function has a single root at that cannot be bracketed. Figure.3.9. Function has no root but changes sign. Explanation Source code for False position method: Example code of False-position method C code was written for clarity instead of efficiency. It was designed to solve the same problem as solved by the Newtons method and secant method code: to find the positive number x where cos(x) = x3. This problem is transformed into a root-finding problem of the form f(x) = cos(x) x3 = 0. #include #include double f(double x) { return cos(x) x*x*x; } double FalsiMethod(double s, double t, double e, int m) { int n,side=0; double r,fr,fs = f(s),ft = f(t); for (n = 1; n { r = (fs*t ft*s) / (fs ft); if (fabs(t-s) fr = f(r); if (fr * ft > 0) { t = r; ft = fr; if (side==-1) fs /= 2; side = -1; } else if (fs * fr > 0) { s = r; fs = fr; if (side==+1) ft /= 2; side = +1; } else break; } return r; } int main(void) { printf(%0.15fn, FalsiMethod(0, 1, 5E-15, 100)); return 0; } After running this code, the final answer is approximately 0.865474033101614 Example 1 Consider finding the root of f(x) = x2 3. Let ÃŽÂ µstep = 0.01, ÃŽÂ µabs = 0.01 and start with the interval [1, 2]. Table 1. False-position method applied to f(x)  =  x2 3. a b f(a) f(b) c f(c) Update Step Size 1.0 2.0 -2.00 1.00 1.6667 -0.2221 a = c 0.6667 1.6667 2.0 -0.2221 1.0 1.7273 -0.0164 a = c 0.0606 1.7273 2.0 -0.0164 1.0 1.7317 0.0012 a = c 0.0044 Thus, with the third iteration, we note that the last step 1.7273 à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ 1.7317 is less than 0.01 and |f(1.7317)| Note that after three iterations of the false-position method, we have an acceptable answer (1.7317 where f(1.7317) = -0.0044) whereas with the bisection method, it took seven iterations to find a (notable less accurate) acceptable answer (1.71344 where f(1.73144) = 0.0082) Example 2 Consider finding the root of f(x) = e-x(3.2 sin(x) 0.5 cos(x)) on the interval [3, 4], this time with ÃŽÂ µstep = 0.001, ÃŽÂ µabs = 0.001. Table 2. False-position method applied to f(x)  = e-x(3.2 sin(x) 0.5 cos(x)). a b f(a) f(b) c f(c) Update Step Size 3.0 4.0 0.047127 -0.038372 3.5513 -0.023411 b = c 0.4487 3.0 3.5513 0.047127 -0.023411 3.3683 -0.0079940 b = c 0.1830 3.0 3.3683 0.047127 -0.0079940 3.3149 -0.0021548 b = c 0.0534 3.0 3.3149 0.047127 -0.0021548 3.3010 -0.00052616 b = c 0.0139 3.0 3.3010 0.047127 -0.00052616 3.2978 -0.00014453 b = c 0.0032 3.0 3.2978 0.047127 -0.00014453 3.2969 -0.000036998 b = c 0.0009 Thus, after the sixth iteration, we note that the final step, 3.2978 à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ 3.2969 has a size less than 0.001 and |f(3.2969)| In this case, the solution we found was not as good as the solution we found using the bisection method (f(3.2963) = 0.000034799) however, we only used six instead of eleven iterations. Source code for Bisection method #include #include #define epsilon 1e-6 main() { double g1,g2,g,v,v1,v2,dx; int found,converged,i; found=0; printf( enter the first guessn); scanf(%lf,g1); v1=g1*g1*g1-15; printf(value 1 is %lfn,v1); while (found==0) { printf(enter the second guessn); scanf(%lf,g2); v2=g2*g2*g2-15; printf( value 2 is %lfn,v2); if (v1*v2>0) {found=0;} else found=1; } printf(right guessn); i=1; while (converged==0) { printf(n iteration=%dn,i); g=(g1+g2)/2; printf(new guess is %lfn,g); v=g*g*g-15; printf(new value is%lfn,v); if (v*v1>0) { g1=g; printf(the next guess is %lfn,g); dx=(g1-g2)/g1; } else { g2=g; printf(the next guess is %lfn,g); dx=(g1-g2)/g1; } if (fabs(dx)less than epsilon {converged=1;} i=i+1; } printf(nth calculated value is %lfn,v); } Example 1 Consider finding the root of f(x) = x2 3. Let ÃŽÂ µstep = 0.01, ÃŽÂ µabs = 0.01 and start with the interval [1, 2]. Table 1. Bisection method applied to f(x)  =  x2 3. a b f(a) f(b) c  =  (a  +  b)/2 f(c) Update new b à ¢Ã‹â€ Ã¢â‚¬â„¢ a 1.0 2.0 -2.0 1.0 1.5 -0.75 a = c 0.5 1.5 2.0 -0.75 1.0 1.75 0.062 b = c 0.25 1.5 1.75 -0.75 0.0625 1.625 -0.359 a = c 0.125 1.625 1.75 -0.3594 0.0625 1.6875 -0.1523 a = c 0.0625 1.6875 1.75 -0.1523 0.0625 1.7188 -0.0457 a = c 0.0313 1.7188 1.75 -0.0457 0.0625 1.7344 0.0081 b = c 0.0156 1.71988/td> 1.7344 -0.0457 0.0081 1.7266 -0.0189 a = c 0.0078 Thus, with the seventh iteration, we note that the final interval, [1.7266, 1.7344], has a width less than 0.01 and |f(1.7344)| Example 2 Consider finding the root of f(x) = e-x(3.2 sin(x) 0.5 cos(x)) on the interval [3, 4], this time with ÃŽÂ µstep = 0.001, ÃŽÂ µabs = 0.001. Table 1. Bisection method applied to f(x)  = e-x(3.2 sin(x) 0.5 cos(x)). a b f(a) f(b) c  =  (a  +  b)/2 f(c) Update new b à ¢Ã‹â€ Ã¢â‚¬â„¢ a 3.0 4.0 0.047127 -0.038372 3.5 -0.019757 b = c 0.5 3.0 3.5 0.047127 -0.019757 3.25 0.0058479 a = c 0.25 3.25 3.5 0.0058479 -0.019757 3.375 -0.0086808 b = c 0.125 3.25 3.375 0.0058479 -0.0086808 3.3125 -0.0018773 b = c 0.0625 3.25 3.3125 0.0058479 -0.0018773 3.2812 0.0018739 a = c 0.0313 3.2812 3.3125 0.0018739 -0.0018773 3.2968 -0.000024791 b = c 0.0156 3.2812 3.2968 0.0018739 -0.000024791 3.289 0.00091736 a = c 0.0078 3.289 3.2968 0.00091736 -0.000024791 3.2929 0.00044352 a = c 0.0039 3.2929 3.2968 0.00044352 -0.000024791 3.2948 0.00021466 a = c 0.002 3.2948 3.2968 0.00021466 -0.000024791 3.2958 0.000094077 a = c 0.001 3.2958 3.2968 0.000094077 -0.000024791 3.2963 0.000034799 a = c 0.0005 Thus, after the 11th iteration, we note that the final interval, [3.2958, 3.2968] has a width less than 0.001 and |f(3.2968)| Convergence Rate Why dont we always use false position method? There are times it may converge very, very slowly. Example: What other methods can we use? Comparison of rate of convergence for bisection and false-position method

Carib Studies Ia

Acknowledgement Nobly, the researcher would like to bestow gratitude to all who has helped me in the completion of this Internal Assessment. Gratitude and appreciation to, God most of all, because without him there's is no ability to complete something. He helped to guide the researcher and helped her put away her indolence and complete her study effectively. The youngest sister of the researcher deserves appreciation because she helped the researcher in getting references and gathering the essential for this project. Much love to you, Lisan.To all those such as my peers and respondents to my questionnaire, Merci. Hope to submissively return the favour one day. Introduction Locale: Urban Parish: St. Ann School Code: 06063 Gender: Female School Organization: Whole Day Size: Class III Attendance Rate: 92% Capacity: 1000 Enrolment: 950 Number of Teachers: 41 Pupil/Teacher Ratio: 24:1 Owned by: Anglican Church Socio-Economic Context St. Hilda’s Diocesan High School for girls was e stablished by the Anglican Church in 1906 as a small day school run by the Deaconesses.In 1917, it was named The Diocesan High School for Girls and moved to its present site in 1922. It was given the present name in 1927. St. Hilda’s is located in Browns Town, St. Ann. It is a medium sized boarding school with approximately 950 students, and it has a capacity of 1000. With 41 teachers, the student teacher ratio is 24:1. The school’s average daily attendance is 92 per cent. Students are from mixed socio economic backgrounds drawn from all over the island and include a few who are not Jamaicans. Many parents are unemployed but some are professionals. Some work in the hotel industry, some are farmers.The school motto: Res Severa Verum Gaudium (Hard work brings true joy) is a source of inspiration for staff and students alike and summarizes the school’s general attitude towards its endeavours and accomplishments. St. Hilda’s High school gets valuable support from business and community organizations in the forms of donations and scholarships. Its high academic standard is complemented by a rich cultural heritage which is showcased in its annual Eisteddfod. In 2010, the school was placed fourth in the ‘All Together Sing’ choir competition and came first in Bob Marley’s Song Arrangement Competition.For the latter, the school received a replica of the icon’s guitar. Intervention programmes like ‘Young women of Change’ give support to students with emotional and social needs. Statement of problem What is the extent of racism at St. Hilda’s Diocesan High, Brown’s Town? Aims and objectives Racism is vastly evident at this institution. The completion of this IA will therefore determine: The extent of racism at the institution The influence of racism at the institution The consequences of racism at the institution Literature review Racism is the ideologies of social processes which discrimin ate against people based solely on the basis of their belonging to different ethnicity. It should be noted that some sociologists such as Parsons, think that people are primarily socialized to be racist. The influencing factors of racism are: parents, siblings, peers, schools, governmental officials, religion, mass media and many others’ (Solomos, 1993, Haralambos and Holborn, 2004). ‘Racial disadvantages are a result of the differences in cultural characteristics that do not coincide with the norms and values of the upper class’ (Smith, N. D adopted from Mustapha, 2009). for integration in the creolization process to take place multi- culturalism and plurality of cultures must be first accepted in order to reduce racial stigmatization (Braithwaite, adopted from Mustapha, 2009). ‘Similarly, functionalists aim for a cultural consensus for a consequential balanced and functional society’ (Kirby,1997 adopted from Haralambas and Holborn, 2004). Marx, how ever, views racism as a belief system used to legitimize the exploitation of the lower class citizens by the upper class. ‘ Some sociologists even believe that if capitalism had not developed then racial prejudice, in question, would not exist’ (Kirby et. l 1997; Cox, 1970, Haralambos and Holborn, 2004). ‘Interactionists believes that racial conflict was a result of the deficiency in communication about the variation in the self-conceptualization. In society, race and ethnicity are viewed as variable because they are often being discussed’ (Lal, 1998; Kirby, 1997, Haralambos and Holborn, 2004). ‘Racism was used to validate slavery during colonialism’ (Roleff, 1991). ‘In the 19th century, indentured workers were bought to Trinidad to supplant the Africans on the plantations and there was an immediate awareness of the ethnic differences.Hence, social stratification in the plantation society was based on the differences in the race in societ y. Therefore, race is one of the fundamental factors behind class division in society. ’ (Brereton, 1979 adopted from Reddock and Barrow, 2001). ‘The term race was first used in the 15th century but only grew in importance with the relation to the development of liberalism bought a sense of identity to people, which was intended to bring further improvement of society, along with equality’ (Golberg, Haralambos and Holborn, 2004). Whites in society being superior encouraged racism and racist beliefs in society and the racism led to the limitations in the social life chances of proletariats’ (Golberg, Haralambos and Holborn) ‘Segregation and discrimination in society are also the results of racism’ (Haralambos and Holborn, 20004). ‘Policies can be formulated to enclose equal opportunities and cultural integration such as the Race and Relations Acts’ (Haralambos and Holborn, 2004). ‘The Creolization Thesis proposes the governme nts can promote cultural assimilation and integration in order to have syncretism.A variety of the cultural traits blended together to form a new culture that is satisfactory for all members of society’ (Braithwaite, 1971, Mustapha, 2009). Research Design The term research design may be defined as the scientific data collected. It is from research that theories are derived. Quantitative data was the selected research data since it is general, objective and value free. The statistics of the data gathered can be easily quantified and is used to support the findings of research. Questionnaires were used because they are used for obtaining particular instruments for data collection.The data gathered from the questionnaires would be easily quantified and displayed in various figures and diagrams. The study is based on the degree of the existence of racism at St. Hilda’s Diocesan High. To effectively complete this project, the study was done during the period of November 20t h to November 30, 2012. In order to attain data randomly, the sample population was selected by process. Two out of the fifty questionnaires presented were separately distributed to students from each grade level and class with permission from the school principal and form teachers. SampleA sample may be defined as a portion of a large population and it is often used to represent the large population. For this study, random sampling was used. So two out of fifty questionnaires were to distributed 2 students from each class from each grade level, who willingly participated in the study. This would be considered systematic random sampling. It is considered as such because the subject units were chosen in a logical order. The method of sampling is practical because it is time effective when selecting the same from a large population. Data Collection InstrumentQuestionnaires were used to collect data. The use of questionnaires was both cost effective and time effective. The use of quest ionnaires assured the maintenance of increased objectivity and the accuracy in the study. The data gathered from the questionnaires can be easily quantified. Questionnaire Gender male female How old are you? To what ethnicity do you belong? African Chinese American Mixed Do you know what racism is? If yes, explain. Do you think racism exists at St. Hilda’s Diocesan High? Please explain the reason for your answer. How prevalent is racism at St.Hilda’s Diocesan High? Great extent not a great extent non-existent Does racism at school affect you? If yes, in what way. Would you consider yourself racist? Would you consider any of your friends as racists? Explain answers for both number 7 and 8. Have you ever been involved in any racist activity? Please account for your answer. Have you ever been a victim of racism? If so, how: Persons provoke you about your ethnicity and religion persons ignore your existence and humanity persons demean your ancestry and heritage other. Plea se specify. Does anyone at your school instigate racism?If so, who: academic staff peers principal ancillary staff Do you think racism has a negative impact on students? If yes, in what way: causing students to fail academically because of low self-esteem and confidence emotionally scarring students, especially the younger ones, for life If other, specify. What are some of the methods that could be used to eliminate or reduce racism at St. Hilda’s? How do you think the school on a whole can benefit from the reduction or elimination of racism? Presentation of Findings Figure 1: Students affected and not affected by racism Figure 2: Been vs. haven’t been victims of racism.Figure 3: ways students were victims of racism Figure 4: racism is instigated/ not instigated Figure 5: Does racism has or doesn’t have a negative impact on students? Analysis and Discussion of Findings As seen in figure 1, 10% isn’t affected by racism while 90% is. This shows that general ly, a large percentage of students are affected by racism at St. Hilda’s Diocesan High. The concept behind this question was to ascertain whether multi- culturalism and plurality of cultures are accepted, in order to reduce racial stigmatization as Braithwaite claimed it must in order for integration and prober flow of communication.Without proper communication students’ learning and interpretation of certain matters will be affected. Figure 2 shows the percentage of students who have been victims of racism at St. Hilda’s Diocesan High. The diagram is based on information received from the related question from the questionnaire. The diagram shows that 80% have been and 20% haven’t. figure 3, displays the percentage and different ways in which students are victimized by racism. Its displays that 10% persons demean their ancestry and heritage, 40%, persons provoke them about their ethnicity and religion and 50%, persons ignore their existence and humanity. Figure 4, 5% said no racism isn’t instigated, while a mighty 95% said it is. When asked how and by who, a large number of students stated that it is instigated by the principal in the way she treats certain students because of either their grades or their light coloured skin. One student notably wrote that she thought about becoming a racist so many times because of the way the principal treated her different from all other students. She notably stated that she is of Chinese ethnicity and is academically well of as she is a prefect at the school. She states that ometimes she thinks she is better than other students academically and when it comes to beauty because of how Mrs Johnson, her principal idolizes her. Also certain things that Mrs Johnson would say instilled some kind of racial feelings inside her. This indeed proves that racism is instigated and goes back to: ‘Racism was used to validate slavery during colonialism’ (Roleff, 1991). ‘In the 19th cent ury, indentured workers were bought to Trinidad to supplant the Africans on the plantations and there was an immediate awareness of the ethnic differences.Hence, social stratification in the plantation society was based on the differences in the race in society. Therefore, race is one of the fundamental factors behind class division in society. ’ (Brereton, 1979 adopted from Reddock and Barrow, 2001). This could cause class division yes because this student might think so highly of herself that she will be-little others as it were in slavery days. Also, racism was instigated by planters to cause division and immediate distinction between owner and slaves.Maybe this is the similar to what Mrs Johnson is doing, separating brighter and prettier students from the rest so the less intelligent or less beautiful one will feel inferior as the slaves did to the whites. All this adds to what is seen in Figure 5. There are 8o% of students who are affected negatively by racism and 20% wh ich aren’t. this incorporates Brerton’s prospective on racial and ethnic discrimination, racism between slaves from other ethnic groups based on stratification. Also with regards to Figure 3, Marx perspective that racism is a belief system used to legitimize the exploitation of the lower class can be applied.Students who say they are affected by racism are those who are may belong to different social classes in social hierarchy or may belong to different ethnic groups than those who are not affected. Certain students who are affected may also be considered less academically accomplished to those who are not. Racism has negative effects on students as shown in Figure 5. This according to Lal, is that interactionists believe that racial conflicts were a result of the deficiency in communication about the variation in self- conceptualization. ConclusionIn conclusion, racism impacts negatively on the lives of the young ladies of St. Hilda’s Diocesan High. Racism neg atively affects school interaction, and behaviour of these young ladies. However, as Braithwaite indicates, through formulation of policies, the Government can promote cultural assimilation and integration in order to have syncretism. A variety of cultural traits blended together to form a new culture that is satisfactory for all students of the St. Hilda’s Diocesan High School. Bibliography Barrow C and Reddock R, (Eds. ), 2001Caribbean Sociology: Introductory Recordings. Kingston: Ian Randle Publishers Ltd. Haralambos, M and Holborn, M (Eds. ) 2004 Sociology: Themes and Perspectives. London: Harper Collins Publishers Ltd. Mustapha, N (Eds) 2009. Sociology for Caribbean Students. Kingston: Ian Randle Publishers Ltd. Kerwin, C and Jackson, I, 1996. Sociology for Caribbean Students, Volume 1. Kingston: Ian Randle Publishers Ltd. Table of Contents Topic Page Acknowledgement Introduction Statement of problem Literature review Research design Sample Data collection instrument Pre sentation of findingsAnalysis and discussion of findings Recommendations Limitations Conclusion Bibliography bRecommendations The researcher would recommend: The government implement some non- racist movement within all schools The government go about implementing ways to encourage students in schools and fire any employee at the school who encourages racism The school’s chairman visit the school more often and see just what is going on there, ask the students their opinions on the matter discussed and go about making changes Students appeal to authorities who might help them on the matterLimitations Within the completion of this project the researcher didn’t have any limitations. All resources were at hand especially at home. The researcher should proudly say that she put these resources to good use. This project was well organized and put together because of this. He researcher hopes all readers and the examiner feels the same.

Analysis of Divisional Performance of Asian Paints Ltd

DEPARTMENT OF COMMERCE SCHOOL OF MANAGEMENT PONDICHERRY UNIVERSITY ASSIGNMENT ON ADVANCED COST ACCOUNTING ANALYSIS OF DIVISIONAL PERFORMANCE OF ASIAN PAINTS LTD SUBMITTED TO: -SUBMITTED BY: – DR. G. SHANMUGHASUNDARAM A. PURUSHOTHAMAN ASSOCIATE PROFESSOR M. COM (BUSINESS FINANCE) DEPT. OF COMMERCE 2nd YEAR PONDICHERRY UNIVERSITY REG. NUMBER: 11351059 INTRODUCTION DIVISIONAL PERFOMANCE OF COST CENTRE AND PROFIT CENTRE A profit centre is a unit of a company that generates revenue in excess of its expenses. The main aim of profit centre is to earn profit.The performance of profit centre is evaluated in terms of whether the centre has been achieved its budgeted profit A  cost centre  is a business unit that is only responsible for the  costs  that it incurs. The manager of a cost centre is not responsible for  revenue  generation or asset usage. The performance of a cost centre is usually evaluated through the comparison of  budgeted  to actual costs. The costs incu rred by a cost centre may be aggregated into a  cost pool  and allocated to other business units. Investment centre is responsible for both profit and investment.The investment centre manager has control over revenue, expenses and the amount invested in the current assets. The following are the techniques used to measure the divisional performance of cost centre and profit centre * Variance analysis * Profit * Return on investment * Market share COST PER UNIT: Cost refers to the total cost incurred for the production. So cost per unit refers to the cost incurred for producing 1 unit. Normally we used the below formula to calculate the cost per unit Cost/unit = total cost / No. of unit produced COST PER UNIT year| Production| Total expenses| COST PER UNIT| 008| 40946. 7| 559586| 0. 073173203| 2009| 50418. 7| 602922| 0. 083623918| 2010| 57937. 2| 732142| 0. 079133829| 2011| 72582. 9| 849056| 0. 085486587| Interpretation: The above table and chart shows the cost per unit of Asian p aints India ltd. They incurred highest cost per unit in the year 2011. This may because increasing the cost of raw material or other charges etc. It is better to have lower cost per unit because when cost per unit increases the total cost will increase. That in turn reduces the profitability of a firm. In the 2008 the firms have lower cost per unit of production compared to other years.So may be this year the profit is increased. The cost per unit is higher in the years 2011 and 2009. COST VARIANCE Cost variance (CV) is the amount of money that was actually spent on a project or a part of a project compared to the amount of work that was actually accomplished. Cost variance = Budgeted cost of work performed – The actual cost of work performed. YEAR| TOTAL COST| STANDARD| COST VARIANCE | DECISION| 2008| 40946. 7| 61276. 54| -20329. 84| A| 2009| 50418. 7| 61276. 54| -10857. 84| A| 2010| 57937. 2| 61276. 54| -3339. 34| A| 2011| 72582. 9| 61276. 54| 11306. 6| F| 2012| 84,497. 20| 61276. 54| 23220. 66| F| Interpretation: Here from 2008 to 2010 there is a favorable situation because in these years actual cost is less than standard cost. In 2011 and 2012 actual cost exceeds standard cost. That may be because of increase in the cost/unit in these years. SALES VARIANCE Sales variance is the difference between actual sales and budget sales. It is used to measure the performance of a sales function, and/or analyze business results to better understand market conditions. Sales variance = Actual sales – standard sales Segment 1= PaintYEAR| SALE| STANDARD| SALES VARIANCE| DECISION| 2008| 39062. 2| 51731. 3| -12669. 1| A| 2009| 48641. 9| 51731. 3| -3089. 4| A| 2010| 56135| 51731. 3| 4403. 7| F| 2011| 63086. 1| 51731. 3| 11354. 8| F| Segment 2= Others YEAR| SALE| STANDARD| SALES VARIANCE| DECISION| 2008| 1731. 7| 1717. 375| 14. 325| F| 2009| 1634. 5| 1717. 375| -82. 875| A| 2010| 1774| 1717. 375| 56. 625| A| 2011| 1729. 3| 1717. 375| 11. 925| A| TOTAL SALES VARI ANCE YEAR| TOTAL SALES| STANDARD| COST VARIANCE | DECISION| 2008| 40,946. 70| 62,655. 72| -21,709. 02| A| 2009| 50,418. 70| 62655. 72| -12,237. 02| A| 2010| 57,937. 0| 62655. 72| -4,718. 52| A| 2011| 72,582. 90| 62655. 72| 9,927. 18| F| 2012| 91,393. 10| 62655. 72| 28,737. 38| F| INTERPRETATION Sales variance is higher in the year 2012 which means that company sold more than standard sales in the year 2012. And the 2011 also have the favorable value but it is lower than 2012. From 2008 to 2010 company cannot sold more than standard sales. That is an unfavorable situation for the company. MARKET SHARE The percentage of an industry or market's total sales that is earned by a particular company over a specified time period is known as market share.Market share is calculated by taking the company's sales over the period and dividing it by the total sales of the industry over the same period. This metric is used to give a general idea of the size of a company to its market and its compet itors. Market share Year| Total sales| Industrial sales| Market share | 2008| 40,946. 70| 348047| 11. 76| 2009| 50,418. 70| 393266| 12. 82| 2010| 57,937. 20| 260717| 22. 22| 2011| 72,582. 90| 834703| 8. 70| 2012| 91,393. 10| 868,234. 00| 10. 53| Interpretation: Company has highest market share in the year 2010. It is decreased in the subsequent years may be because of increased price of the products.WORKING CAPITAL TURN OVER RATIO A measurement comparing the depletion of working capital  to the generation of sales over a given period called as working capital turn over ration. This  provides some useful information  as to how effectively a company is using  its working capital to generate sales. WORKING CAPITAL TURN OVER RATIO YEAR| TOTAL SALES| CURRENT ASSETS| CURRENT LIABILITIES| WC| WCTOR| 2008| 40,946. 70| 8,686. 30| 8018. 6| 667. 70| 61. 32| 2009| 50,418. 70| 10,403. 70| 7811. 4| 2,592. 30| 19. 45| 2010| 57,937. 20| 11,981. 00| 10588. 7| 1,392. 30| 41. 61| 2011| 72,582. 90| 15,475. 70| 11952. | 3,522. 90| 20. 60| 2012| 91,393. 10| 19,927. 70| 16008. 9| 3,918. 80| 23. 32| Interpretation: Here working capital ratio is higher in the year 2008. This means that company may have adequate working capital for their operation in 2008. Working capital to ratio is very lower in the subsequent years (i. e. 2009 to 2012), it shows that company is struggled with inadequacy of working capital in that years. INVENTORY TURN OVER RATIO Inventory Turnover Ratio is one of the efficiency ratios and measures the number of times, on average, the inventory is sold and replaced during the fiscal year.Inventory Turnover Ratio formula is: year| Total sales| opening stock| closing stock| Avg stock| ITOR| 2008| 40,946. 70| 40,946. 70 | 42,954. 70 | 41,950. 70 | 97. 61| 2009| 50,418. 70| 50,418. 70 | 52,427. 70 | 51,423. 20 | 98. 05| 2010| 57,937. 20| 57,937. 20 | 59,947. 20 | 58,942. 20 | 98. 29| 2011| 72,582. 90| 72,582. 90 | 74,593. 90 | 73,588. 40 | 98. 63| INTERPRETATIONA low inventory turnover ratio is a signal of inefficiency, since inventory usually has a rate of return of zero. It also implies either poor sales or excess inventory. A low turnover rate can indicate poor liquidity, possible overstocking, and obsolescence, but it may also reflect a planned inventory buildup in the case of material shortages or in anticipation of rapidly rising prices. In our case the 2008 has the lower turnover rate. A high inventory turnover ratio implies either strong sales or ineffective buying (the company buys too often in small quantities, therefore the buying price is higher).A high inventory turnover ratio can indicate better liquidity, but it can also indicate a shortage or inadequate inventory levels, which may lead to a loss in business. Here the years from 2009 to 2011 there is constant turnover rate. RETURN ON INVESTMENT A performance measure used to evaluate the efficiency of an  investment or to compare the efficiency of a number of different inves tments. The objective of every firm is to earn a satisfactory return on capital invested. This is the measure of success i. e. it shows the overall profitability of the firm. ROI = PAT/ cap. Employed YEAR| PBIT| CAPILAT EMPLOYED| ROI| 2008| 5925. | 9,285. 00| 63. 81583199| 2009| 6075. 9| 10,944. 70| 55. 51454128| 2010| 10526. 9| 15,572. 20| 67. 60059593| 2011| 11636. 7| 19,753. 20| 58. 91045501| 2012| 14,086. 30| 24,877. 80| 56. 62196818| INTERPRETATION The above table and chart implies us, The ROI is higher in the year 2008. The Company gets 63. 82% as return on investment. This may because; in this year company sold more than the standard sales. So return on investment is increased. Company received lowest ROI in the year 2009 CONCLUSION: The Asian paints ltd is having an indifferent performance levels, they have both positive and negative performance indicators.The sales variance is for the last two years is favorable for the company, and also all other indicators such as cost va riance favorable for the firm. Another thing is that market share of the company shows a decreasing trend due to decrease in sales. The inventory and working capital of the company is also not good. So it is important for the company to focus on to improve sales volume with higher turnover, better maintenance of working capital. And to try to get more return on investment by adopt necessary measure and techniques.

Germanic Culture Preserved in Beowulf - 1284 Words

Germanic Culture Preserved in Beowulf Many differences can be found between early Germanic culture and our culture today. Beowulf,the story of the triumphs of a great warrior over near impossible feats, takes place in Scandanavia during the 450s. In this tale, the war obsessed men exhibit values important to the early Germanic culture. Recording such an epic tale not only immortalizes the hero of the poem, but in turn also makes certain that these Scandanavian ways of life will never be forgotten. Their morals, while on the surface seem wrong compared to those found in society today, make sense to them because of the unwritten rules they have set up. The differences in these cultures make it difficult for people today to find interest†¦show more content†¦Throughout the story, the text brings out the value of revenge through Grendel s mother avenging her son, the tale of Herebeald and Haetheyn told by Beowulf, and the effects that death has on other characters. Revenge can be a way people in this time period to honor the memory of a fallen kinsman. With no legal system like that of which can be found in American society today, the only way they see fit to find justice for the crime of murder comes from murdering those responsible. This cycle, while seemingly never ending, can be stopped by paying a weregild, or an amount of money giving to absolve one of a crime they have committed. This speaks volumes of the importance of vengeance over the death of a kin, considering the great value money has to this culture. One example of this, the death of a man in the Geats party during the fight with Grendel. Beowulf makes it clear that he expects a payment from Hrothgar, which shows that the price put on the life of a man comes before keeping his memory alive once he passes. While weregild can be used to deal with death, the other would be to kill the responsible party. This task usually falls on the kin of the deceased, just as Grendel s mother avenges the death of her son after his death at the hands of Beowulf. There are instances where these two options do not apply. Beowulf tells the tale of brothers HerebealdShow MoreRelatedAnglo-Saxon Heroic Poetry5673 Words   |  23 PagesOld English poetry is divided into two types: the Heroic, the sources of which are pre-Christian Germanic myth, history and custom; and the Christian. Heroic, or Epic Poetry belongs to one of these two types and refers to long narrative poems celebrating the great deeds of one or more legendary heroes, in a grand, ceremonious style. In its strict use by literary critics, the terms Heroic Poetry or Epic are applied to a work that meets the following criteria: such a poem must be related in anRead MoreHistory Of Ancient Poetry Ghosh ( 1 )995 Words   |  4 Pageswas characterized by foreign invasions and internal struggles. This resulted within the admixture of many races, tongues and cultures. Once the Romans departed from British Isles in 407 AD fighting continuing between the Picts and therefore the Scots who had lost their common enemy. The fifth century additionally saw conquests and therefore the gradual occupation by Germanic tribes - Angles, Jutes and Saxons - who had rapt north to Scandinavia and from there to Great Britain aside from creating conquestsRead More The Anglo-Saxon poems, The Wanderer, The Seafarer, and The Wife’s Lament3469 Words   |  14 Pagesculture’s societal structure, and religious struggle of the Old English time period: making the transition from paganism to Christianity. In order to understand how these poems mirror the Anglo-Saxons’ lives, one must know a little history about the culture. In the fifth century, the inhabitants of the island of Britain hired German mercenaries to defend them against their warring neighbors, the Picts and the Scots. 2 After having defeated the enemies, the pagan Angles, or Saxons, revolted against theirRead MoreQuestion and Correct Answer7042 Words   |  29 PagesWorld culture quiz ï‚ · Question 1 2 out of 2 points | | | Why did the arts develop in Mesopotamia?Answer | | | | | Selected Answer: |   Ã‚   As celebrations of the priest-kings power | Correct Answer: |   Ã‚   As celebrations of the priest-kings power | | | | | ï‚ · Question 2 2 out of 2 points | | | What did lost-wax casting enable the Mesopotamian sculptors to create?Answer | | | | | Selected Answer: |   Ã‚   Larger and more lightweight bronze pieces | Correct Answer: |   Ã‚   Larger