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Advanced Business Mathematics covers various different types of topic areas. However, the assignment only allows showing all the calculation/workings/formula for introducing to Management Statistics, Regression, Time Series, and Inferential Statistics, etc.

This research paper aims at achieving significant understanding of each topic area as we go along while providing an outline of notes from NCC education for indulgence as the mission and responsibilities is to accomplish the knowledge and understanding of the project.

Advanced Business Mathematics typically uses in commerce which includes more of probability, statistics, linear programming. Calculus is a more effective topic use in some cases of Advanced Business Mathematics, but not being asked to research on in the given assignment.

Further on in the project you will read and get the more knowledge and understanding of each particular calculation headings. The references provide opportunity for further knowledge on the concepts of the different types of calculation in the paper.

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Project Background

Arithmetic

Algebra

Statistic

Probability

However, Advanced Business Mathematics can be more effective at times in some cases by using more of calculus, matrix algebra and linear programming. Most business organizations use mathematics in accounting, inventory management, marketing, and as well as financial analysis, etc. But mainly used for commercial enterprise purposes by recording the correct calculations in order to manage business operations.

In effect, Advanced Business Mathematics in this field is an important subject taught, and the knowledge of it will enhance ones' reasoning: the process of taking in information and making inferences based on what an individual knows to be true. Thus, a gauge of one's intellectual abilities, reasoning enables people to understand ideas and concepts better, and arrive at logical conclusions, problem-solving: try looking at existing solutions to common problems, e.g. design patterns. Maybe something similar will pop up that at least partially resemble the given problem, and the liability to think effective: the ability to apply the reasoning and logical to new or unfamiliar ideas, opinions, and solutions. In effect, try to see things in an open-minded way examining an idea or concept from as many angles possible. Hence, the mathematic tools are needed such as the; calculator, understanding, knowledge, time management, etc. in order to perform a good task.

Literature Review

Researcher argued that to understand the use of Advanced Business Mathematics, one needs to know little bit about how to conduct an investigation. In other words, since statistic are not just numbers that just appear out of nowhere, one should know the understanding of the topic in order to complete the assignment.

Dantzig, who turned 80 on November 8, is generally regarded as one of the founders of linear programming, along with von Neumann and Kntovich. Through his research in mathematical theory, computation, economic analysis, and applications to industrial problems, he has contributed more than any other researcher to the remarkable development of linear programming. In 1993 he said that linear programming is the capacity to solve the problems which originated. Linear programming and its offspring have come to of age and have demonstrably passed the test, and they are fundamentally affecting the economic practice of organization and management.

Eugene Lawler argued that linear programming is used to allocate resources, plan production, schedule workers, plan investment portfolios and formulate marketing strategies.

In addition, Advanced Business Mathematics is way different in coursework from a basic or regular mathematics coursework. In other words, in a regular mathematics coursework, there would be more concentrating on trigonometry rather than probability and so on for Advanced Business Mathematics. However, a more effective mathematics coursework in this level requires more Advanced Business Mathematics level such as, linear programming, regression, time series, and inferential statistic, etc.

Objectives

To familiarize ones' with the concepts and tools of Advanced Business Mathematics as applicable to decision in a business environment.

To provide quantitative skills which can be used in the assignment in order for one's to formulate, use and interpret mathematical models within a business context.

Understand applications of the learned mathematical principle.

Methodology

Advanced Business Mathematics is now used in most aspects of daily life. Thus, the researcher employed quantitative method to carry out the research; the quantitative research methods which includes both primary and secondary sources in order to gear towards the correct calculations of each heading, as well as for one's to formulate, use and interpret mathematical models within a business context.

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Primary sources such as the student which have direct knowledge and the understanding of how to go about on calculating the given problems of the particular headings with the aid of getting information from the NCC education notes and lecturer notes as well. This type of source was chosen because without ones' getting the understanding and knowledge on the concept of a particular heading, there won't be a completion of the assignment. In effect, the key to motivation is understanding, and this will state whether or not the power to change both expectations of self and the value placed on attempting the task given.

Secondary sources included textbooks, references, and the internet which were used to attempt to the problems on how to go about calculating the workings given in the research paper. These secondary sources are very effective to the assignment given. Thus, it involved generalization, analysis, interpretation, or evaluation of the original information. These secondary sources are contrasts with the primary sources. In other words, they provide opportunity for further knowledge on the concepts of preparing the calculations.

Question 1

Introducing to Management Statistics

Observations (x)

Frequency (f)

FX (f)(x)

10

4

40

15

5

75

20

9

180

40

16

640

60

8

480

80

5

400

100

3

300

Calculate;

Mean

Mode

∑ƒáµª

ƒ(n)

= 2115

50

## Mode

Counting: 40

10

15

20

15

20

40

40

60

40

15

10

15

40

40

20

60

80

60

20

40

10

20

60

60

80

40

100

40

20

40

10

20

40

40

60

40

40

40

20

15

40

20

60

40

60

80

100

80

100

80

Question 1.2

Regression

Days of the month

Total sale of the product A (X)

Total sale of the product B (Y)

XY

X2

Y2

1st day

15

16

240

225

256

4th day

14

13

182

196

169

7th day

10

11

110

100

121

10th day

18

19

342

324

361

15th day

15

13

195

255

169

18th day

20

22

440

400

484

22nd day

16

15

240

256

225

25th day

5

117

255

225

289

27th day

12

16

192

144

256

30th day

13

17

221

169

289

TOTAL

MEAN

## 241.7

Calculating the r (correlation) between x and y;

R= r = n∑x;y; - ∑x;∑y;

(n∑x;-(∑x;(2 n)∑y;)2-(∑y;)2(

= 10(2417)-(148*159)

10(2264-(148)2 (10(2619-159)2)

= 24170-23,532

(22,640-21904)(26190-25281)

= 638

(736)(909)

= 638

669,024

= 638

817.938873

## = 0.78

Question 2.1

Calculate the Laspeyres and Paache price indices for the following data. Take from 2005 as the base year.

Litre of beer

Litre of Whiskey

Litre of wine

Year

Price

Qty

Price

Qty

Price

Qty

2005

0.95

200

19.80

10

10.50

36

2006

0.99

150

20.39

12

11.15

48

2007

1.05

120

20.99

11

12.35

60

## ∑q0 P0

LPI05 = ∑q05 P05 * 100

∑q05 P05

= (200*0.95) + (10*19.80) + (36.10.50) *100

(200*0.95) + (10*19.80) + (36.10.50)

= 190 + 198 + 378 *100

190 + 198 + 378

= 766 *100

766

## = 100%

LPI06 = ∑q05 P06 * 100

∑q05 P05

= (200*0.99) + (10*20.39) + (36*11.15) *100

(200*0.95) + (10*19.80) + (36.10.50)

= 198 + 203.9 + 401.4 *100

190 + 198 + 378

= 803.3 *100

766

## = 104.8%

LPI07 = ∑q05 P07 * 100

∑q05 P05

= (200*1.05) + (10*20.99) + (36*12.35) *100

(200*0.95) + (10*19.80) + (36.10.50)

= 210 + 209.9 + 44.6 *100

190 + 198 + 378

= 864.5 *100

766

## ∑pn Po

PPI= ∑q05 P05*100

∑p05 P05

= (200*0.95) + (10*19.80) + (36*10.50)*100

(200*0.95) + (10*19.80) + (36*10.50)

= 190 + 198 + 378 * 100

190 + 198 + 378

= 766 *100

766

## = 100%

PPI= ∑q05 P05*100

∑p05 P05

= (150*0.99) + (12*20.39) + (48*11.15) *100

(150*0.95) + (12*19.80) + (48*10.50)

= 148.5 + 244.68 + 535.2 *100

142.5 + 237.6 + 504

= 928.38 * 100

884.1

## = 105%

PPI= ∑q05 P05*100

∑p05 P05

= (120*1.05) + (11*20.99) + (60*12.35) *100

(120*0.95) + (11*19.80) + (60*10.50)

= 126 + 230.89 + 741 *100

114 + 217.8 + 630

= 1097.89 *100

961.8

## = 114%

Question 2.2

Time series

The number of rats captured in a grain store is summarized below. Use simple exponential smoothing with alpha = 0.2 and alpha = 0.7 to forecast the number of rats that will be caught in week 7.

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Alpha 0.2

Alpha 0.7

Week 1

216

216

216

Week 2

224

216

216

Week 3

217

217.6

221.6

Week 4

233

217.5

218.4

Week 5

245

220.6

228.6

Week 6

229

225.5

240.1

Week 7

Alpha 0.2

## Formula: ft+1= αYt + (1-α)Ft

Week 2

F2= 0.2 Y1 + (1-0.2) F1

F2= 0.2(216) + 0.8 (216)

F2= 43.2 + 172.8

F2= 216

Week 3

F3= 0.2 Y2 + (1-0.2) F2

F3= 0.2(224) + 0.8 (216)

F3= 44.8 + 172.8

F3= 217.6

Week 4

F4= 0.2 Y3 + (1-0.2) F3

F4= 0.2(217) + 0.8 (217.6)

F4= 43.4 + 174.08

F4= 217.48

Week 5

F5= 0.2 Y4 + (1-0.2) F4

F5= 0.2(233) + 0.8 (217.48)

F5= 46.6 + 17.4

F5= 220.584

Week 6

F6= 0.2 Y5 + (1-0.2) F5

F6= 0.2(245) + 0.8 (220.584)

F6= 49 + 176.48

F6 = 225.4672

Week 7

F7= 0.2 Y6 + (1-0.2) F6

F7= 0.2(229) + 0.8 (225.5)

F7= 45.8 + 180.4

F7= 226.2

Alpha 0.7

## Formula: ft+1= αYt + (1-α)Ft

Week 3

F3= 0.7Y2 + (1-0.7) F2

F3 = 0.7 (224) + 0.3 (216)

F3 = 156.8 + 64.8

F3 = 221.6

Week 4

F4= 0.7Y3+ (1-0.7) F3

F4 = 0.7 (217) + 0.3 (221.6)

F4 = 151.9 + 66.48

F4 = 218.38

Week 5

F5= 0.7Y4 + (1-0.7) F4

F5 = 0.7 (233) + 0.3 (218.38)

F5 = 163.1 + 65.52

F5 = 228.614

Week 6

F6= 0.7Y5 + (1-0.7) F5

F6 = 0.7 (245) + 0.3 (228.614)

F6 = 171.5 + 68.58

F6 = 240.0842

Week 7

F7= 0.7Y2 + (1-0.7) F2

F7 = 0.7 (229) + 0.3 (240.0842)

F7 = 160.3 + 72.03

F7 = 232.32526

Question 2.3

Inferential statistics

A cruise ship was interested in the typical duration each client spent in the breakfast buffet. The entry and exist times of 30 cruisers was noted.

Time (minutes) spent dining;

43

35

36

25

30

35

42

28

18

21

39

43

3

38

27

34

28

41

19

44

34

39

19

36

29

33

24

40

31

18

Calculate and approximately 99% confidence interval for the mean breakfast time.

43 + 35 + 36 + 25 + 30 + 35 + 42 + 28 + 18 + 21 + 39 + 43 +34 + 38 + 41 + 19 + 44 + 34 + 39 + 19 + 36 + 29 + 33 + 24 + 40 + 31 + 18

30

X= 973

30

X = 32.43

S2 = ∑;-1(χ;-χ)2

n-1

S2= (43-32.43)2 + (35-32.43)2+ (36-32.43)2 + (25-32.43)2 + (30-32.43)2 + (35-32.43)2 + (42-32.43)2 +( 28-32.43)2 + (18-32.43)2 +( 21-32.43)2 + (39-32.43)2 +( 43-32.43)2 +(34-32.43)2 + (38-32.43)2 + (27-32.43)2 + (34-32.43)2 + (38-32.43)2 + (41-32.43)2 + (19-32.43)2 + (44-32.43)2 + ( 34-32.43)2 + (39-32.43)2 + (19-32.43)2 + (36-32.43)2 + (29-32.43)2 + (33-32.43)2 + (24-32.43)2 + (40-32.43)2 + (31-32.43)2 + (18-32.43)2

30-1

S2= (10.57)2+ (2.57)2 + (3.57)2 + (-7.43)2 + (-2.43)2 + (2.57)2 + (9.57)2 + (-4.43)2 + (-14.43)2 + (-11.43)2 + (6.57)2 + (10.57)2 + (1.57)2 + ( 5.57)2 + (-5.43)2 + (1.57)2 + (5.57)2 + (8.57)2 + (-13.43)2 + (11.57)2 + (1.57)2 + (6.57)2 + (-13.43)2 + (3.57)2 + (-3.43)2+ (0.57)2 + (-8.43)2 + (7.57)2 + (-1.43)2 + (-14.43)2

29

S2 =111.7249 + 6.6049 + 12.7449 + 55.2049 + 5.9049 + 6.6049 + 91.6249 + 208.2249 + 130.6449 + 43.1649 + 111.7249 + 2.4649 + 31.0249 + 29.4849 + 2.4649 + 31.0249 + 73.4449 + 180.3649 + 133.8649 + 2.4649 + 43.1649 + 180.3649 + 12.7449 + 11.7649 + 0.3249 + 71.0649 + 57.3049 + 2.0449 + 208.2249

29

S2= 1,927.367

29

S2 = 66.461

Std dv = 66.461

## Formula: X±Zαz(s n)

χ = 32.43

n = 30

S = 8.15

Zα = 2.5758/2.58 (ROUND OFF)

= 32.43±2.58*8.15

30

= 32.43±21.027

5.4772

= 32.43±3.839

= 32.43 + 3.839

= 32.43 - 3.839

## = 28.591

99% confident that the estimate of the mean breakfast time is between 28.591 and 36.269.

Question 2.4

Linear Programming

Minimize; cost = 9x + 3y

Subject to the following constraints;

Constraints 1: Y ≥ 5

Constraints 2: 6X + 7Y ≥ 210

Constraints 3: 7X + 15Y ≤ 525

Constraints 4: 5X + 28Y ≤ 700

Constraints 5: X ≥ 0, Y ≥ 0

Which of the following constraints are binding and non-binding?

Solving minimum cost

Corners

Expression to find minimum cost using 9x + 3y

(30,5)

9(30) + 3(5) =285

(65,5)

9(65) + 3(5) = 600

(10,23)

9(10) + 3(23) = 165

(40,18)

9(40) + 3(18) = 414

MINIMUM COST = 165

Question 2.5

Decision Tree

What is decision tree?

According to Advanced Business Mathematics lecture notes, based on my understanding, a decision tree is a tool that uses a tree-like graph shape. It is also a model of decision and their possible consequences which includes;

Notes which are decision, or choices made, and events.

Braches which re line that shows the sequences of levels and decision made, and routs into the future.

Decision tree is another way to display on algorithm and company used in operations research, specifically in decision analysis to help identify a strategy that must likely to reach goal oriented, for e.g. if a company plans to launch a new product version on the market, the firm would want to know what to be done, and how it should be done in order to geared towards goal oriented.

Using example of a typical decision tree discuss the TWO uses of the decision tree.

Since a company decided to launch a new product version or maintain its existing product version, then the cash flows will depend on the products success or failing ( not known with certainty), but if the old product is maintain by future cash flows, it can then be used to predicted with accuracy, for e.g.

Failure -100

Success 100

Old product 35

In addition, the two uses of the decision tree are to find out;

whether the firm will either have a maximum profit, revenues, values or a minimum for costs and losses to launched the product version or not.

To know if future returns are being described by a probability distribution and if he average value for the future is calculated as well.

Question 2.6

Differentiation

Some people believe that differentiation is just mathematics that involves random calculation. Explain TWO ways in which differentiation can be applied to economic analysis.

In such sense, differentiation states the way through which quality of goods is improved over time. In other words, launching new goods effectively and efficiently is a way by which an increase in radical changes occurring; often lead to changes in market shares, as well as the industry structures.

In effect, applying economic analysis using differentiation, vertical differentiation will be used. However, vertical differentiation occurs in market where several goods that are present can ordered according to the objectives quality.

Findings

The following interpretation was obtained from NCC notes that were sent to email, and from notes that was given in class.

Advanced Business Mathematics covers numerous and various different types of topics. However, the assignment only allows showing all calculation/workings/formula for introducing to Management Statistics, Regression, Time Series, and Inferential Statistics, etc. it is an important function use in business organization these days.

It is designed to ensure that effectiveness and efficiency of operations reliability of proper workings and compliance with applicable laws and regulations.

Advanced Business Mathematics typically uses in commerce which includes more of probability, statistics, linear programming. Calculus is a more effective topic uses in some cases of Advanced Business Mathematics.

Recommendation

The assignment that was done on Advanced Business Mathematics was a challenging act; still, valid and reliable information was gathered. The researcher has nothing but positive comments towards the assignment. However, since Advanced Business Mathematics cover difficult areas the researcher would like to recommend ones' to continue on the same path by doing extremely well; try not getting too comfortable and always searching for improvement. The researcher recommendation to the ones has to relation with another is for them to continue being has responsible and effective when doing their work.

The assignment has accomplished success base on the time management that was put in when attending the assignment.

Conclusion

The following information was interpreted from NCC education (www.nccedu.ccom) notes and notebook. The information conveyed is based on the judgment of management with an appropriate consideration to materiality. In this regard, this project will takes time out for understanding each topics and to ensure that the calculations are properly authorized and recorded. In effect, time management is effective tools that were used in order to complete the assignment.