Mathematics Model

8/10/2019 Mathematics Model

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OCTOBER 2011 P/ID 77508/PMBH/

PMB1H

Time : Three hours Maximum : 100 marks

PART A (5 6 = 30 marks)

Answer any FIVE questions.

All questions carry equal marks.

1. State the conditions for an unbounded solution ofa LPP.

2. What is the use of MODI method?

3. How do you convert an unbalanced transportation

problem into a balanced one?

4. Give an example of first come, last served. Also

explain service system.

5. Distinguish between sequencing and scheduling.

6. What is the significance of float in CPU?

7. State the rule of dominance in game theory.

8. Explain the significance of simulation in model

building.


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PART B (5 10 = 50 marks)



9. Egg contains 6 units of vitamin A per gram and

7 units of vitamin B per gram and cost 12 paise

per gram. Milk contains 8 units of vitamin A pergram and 12 units of vitamin B per gram, and

costs 20 paise per gram. The daily minimum

requirement of vitamin A and vitamin B are

100 units and 120 units respectively. Find the

optimal product mix.

10. Solve :

Max. 321 325 xxxz +=

.0,,

53

343

222toSubject

321

32

21

321

+

+

xxx

xx

xx

xxx

11. Solve the transportation problem

Demand point

Source 1 2 3 4

Supply

1 2 3 11 7 6

2 1 0 6 1 1

3 5 8 15 9 10

Demand 7 5 3 2


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12. Solve the travelling salesman problem for the

given data :

12c = 20; 13c = 4; 14c = 10; 23c = 5; 34c = 6

25c = 10; 35c = 6; 45c = 20 where jiij cc = and there

is no route between cities i and j if a value for ijc

is not shown above.13. A taxi owner estimates from his past records that

the cost per year for operating a taxi whosepurchase price when new is Rs. 60,000 are as

given :Age : 1 2 3 4 5

Operating cost (Rs.) : 10,000 12,000 15,000 18,000 20,000

After 5 years, the operating cost is Rs. 6000 Kwhere, K = 6, 7, 8, 9, 10 (K denoting age in years).

If the resale value decreases by 10% of purchase

price each year, what is the best replacement

policy?14. A company has a demand of 12,000 units/year foran item and it can produce 2000 such items per

month. The cost of one set-up is Rs. 400 and the

holding cost/unit/month is Rs. 0.15. Find theoptimum lot size, maximum inventory and total

time.

15. In a public telephone booth the arrivals are on theaverage 15 per hour. A call on the average takes

3 minutes. If there is a just one phone, find :(a) expected number of callers in the booth at

any time,

(b) proportion of the time the booth is expectedto be idle?


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16. Solve the game graphically.

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PART C (1 20 = 20 marks)

(Compulsory)

17. The activities of a project with normal and crash

time are given below :

Activity Normal Crash

Time

(Hrs.)

Cost

(Rs.)

Time

(Hrs.)

Cost

(Rs.)

12 20 2000 15 3000

13 10 1500 7 2400

25 15 1000 10 1500

34 16 3000 12 4000

35 22 4500 16 5700

45 14 1500 10 2100

Find the optimum scheduling of the project which

minimise the total cost.


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OCTOBER 2011 P/ID 77715/MBN1D


SECTION A (10 3 = 30 marks)

Answer any TEN questions.


Write short notes on the following.

1. Communication process.

2. Written communication.

3. Video conferencing.

4. EPABX.5. ETC.

6. Quotations.

7. Insurance letters.

8. Agenda.

9. Secretarial reports.

10. Circulars.

11. Notices.

12. E-mail.


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SECTION B (5 6 = 30 marks)



13. Describe the basic elements of communication.

14. Describe the demerits of oral communication.

15. Explain the uses of Facsimile System (FAX).

16. Explain the various uses of Electronic Mail inbusiness.

17. Explain the elements of a good letter of complaint.

18. Describe the different kinds of Replies.

19. Explain the guidelines for writing a press report.

20. Describe the various modern forms ofcommunication.

SECTION C (2 20 = 40 marks)

Answer any TWO questions.


21. Communication is as essential as anything

because nothing can be achieved without it.Elucidate the statement underlining theimportance of communication.


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22. Discuss the cost effectiveness of various

communication devices.

23. Draft a letter canceling your order placed some

days earlier. Give reasons for the cancellation.

24. Write as a secretary a letter to a director whomwas absent for a Board Meeting.


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OCTOBER 2011 P/ID 77514/PMBP





1. Explain the various steps involved in the merger

and acquisitions.

2. Differentiate between a business level strategy

and corporate level strategy.

3. What is meant by socialism?

4. Define strategy and list out classifications of

strategies.

5. Why the joint venture is adopted as the best tool

for reaching new market?

6. Explain the concept of portfolio analysis.

7. What is CSR?

8. What are the threats from international activities?


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9. What are the factors which influence strategic

choice?

10. Explain SWOT analysis and its relevance to

strategy formulations.

11. Discuss the different types of diversifications.

12. Define and discuss international environment.

13. How would you implement retrenchment strategy?

14. Define the concepts of creativity and innovation.

15. Write short notes on :

(a) Scope of ethics

(b) Product life cycle

(c) GPI policy.

16. Discuss the nature and scope of corporate

management and its role in non-business

organizations.


Compulsory

17. Each level of strategy involves different strategic

decisions. Illustrate with suitable examples.


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OCTOBER 2011 P/ID 77506/PMBF/

PMB1F





1. Describe

(a) Express contract

(b) Unilateral contract.

2. Enumerate the essential elements of a contract.

3. Describe the types of negotiable instrument.

4. Briefly explain the characteristics of a negotiable

instrument.

5. Distinguish company from partnership.

6. Describe the alteration of memorandum.

7. Enlist the provisions ensuring the health of the

workers in the Factories Act, 1948.

8. Enumerate the calculation of compensation for

permanent total disablement in WorkmensCompensation Act, 1923.


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9. Explain the legal rules as to consideration.

10. Explain the different modes of discharge of acontract.

11. Explain the essentials of a contract of sale.

12. Explain the different modes of discharge of a

negotiable instrument.

13. Explain the characteristics of a company.

14. Explain the contents of a prospectus.

15. Explain the main features of the Industrial

Disputes Act, 1947.

16. Explain the main features of the Payment of

gratuity Act, 1972.

PART C (20 marks)

Compulsory

17. An association of 12 members starts a banking

business without being registered. 4 members

retire and thereafter a suit is instituted by one of

the continuing members for the partition of assets

of the business. Discuss the validity of the suit.


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OCTOBER 2011 P/ID 77504/

PMBD/PMB1D





1. Bring out the scope of management accounting.

2. What is liquidity ratio how do you calculate?

3. Explain the importance of financial statements

analysis.

4. What are the elements of costing?

5. What is break even analysis?

6. Examine the rationale of capital budgeting.

7. Discuss the concept of zero base budgeting.

8. Write a note on process costing?


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9. From the following balances, prepare profit and

loss account on 31.3.2006.Rs.

Gross profit 90,000

Salaries 11,000

Fire insurance premium 3,000

Advertisement 1,000

Trade expenses 500

Carriage outward 5,000

Rent 4,000

Bad debts 2,500

Travelling expenses 2,000

10. Calculate funds from operation from the following

information.

Net profit for the year Rs. 6,50,000

Gain on sale of building Rs. 35,500

Goodwill written off during year Rs. 18,000

Old machinery worth Rs. 8,000 has been sold for

Rs. 6,500 during the year.

Rs. 1,25,000 has been transferred to reserve fund.

Depreciation of assets for the year amountsRs. 15,000.


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11. Calculate (a) current ratio (b) liquidity ratio

(c) proprietary ratio (d) debt-equity ratio with the

help of following information.

Liabilities Amount Assets Amount

Capital 5,00,000 Land and building 6,00,000

Preference

capital

2,00,000 Plant and

machinery

5,00,000

Debentures 4,00,000 Debtors 2,00,000

Reserves 3,00,000 Stock 2,40,000

Creditors 2,00,000 Cash balance 55,000

Prepaid expenses 5,000

16,00,000 16,00,000

12. Calculate (a) profit volume ratio (b) BEP (c) profit

when sales are Rs. 1,00,000. When salesRs. 1,20,000, profit 9,000 and fixed cost

Rs. 20,000?

13. The cost structure of production of 60,000 units is

given below, prepare a budget for 1,00,000 units of

production.

Raw material Rs. 2.50 per unit

Direct labour Rs. 1.00 per unit

Direct expenses Rs. 0.50 per unit.

Work overheads (60% fixed) Rs. 2.00 per unit

Administrative overhead (80% fixed) Re. 1.00 perunit.


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14. Explain how management accounting helps in

decision making.

15. Explain the process of standard costing with its

advantages.

16. Bring out the limitations of managementaccounting.


(Compulsory)

17. A project needs an investment of Rs. 1,38,500. The

cost of capital is 12%. The net cash inflows are as

under.

Year : 1 2 3 4 5

Inflow (Rs.) : 30000 40000 60000 30000 20000

Evaluate the project based (a) ARR and (b) NPV

and suggest whether the project should be

accepted or not.


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OCTOBER 2011 P/ID 77501/PMBA/

PMB1A





1. Write short notes on-scientific management.

2. What is MBO? Explain.

3. Explain about traditional authority.

4. What is encoding and decoding in communication?

5. What is decision-making? Explain its importance?

6. Explain the importance of motivation.

7. Explain the controlling techniques in organisation.

8. Explain the need of co-ordination in organisation.



All questions carry equal marks.9. Explain the basic principles and process of

management.


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10. Write the basic techniques of planning.

11. Explain the concept of psychological hazards and

strategic planning process.

12. What is policy making and write its importance?

13. How will you overcome the barriers of

communication in organisation?

14. Explain the factors to be considered in the

establishment of an organization.

15. Explain the use of organizational charts and

manuals.

16. Explain the advantages of management by

exception.


(Compulsory)

17. Case Study :

Managers are important in setting the ethical tone

for employees. If you work for an unethical

manager, chances is you may eventually feel some

pressure to act in ways that you consider

unethical. When you suspect that your boss is not

completely honest when reporting the sales figuresfor your unit.


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(a) What should you do?

(b) How would you respond?

Your boss maintains that he has been doing

this in the best interest of the company. Is he

right or wrong? If you happen to be the boss

how would you act in the same situation?


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PMBE/PMB1E





1. Describe marginal relationship with example.

2. Describe business indicator with example.

3. Enumerate short run cost function.

4. Draw a break-even chart and explain.

5. Enumerate the uses of input output analysis.

6. How do you measure economic concentration?

7. Explain the measurement of economic effect of

advertisement.

8. Describe :

(a) National income

(b) Consumption


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9. Explain law of demand and the demand elasticity.

10. Explain multivariate optimization techniques.

11. Forecasting methods require modifications withrespect to the object in concern Explain.

12. Explain the uses of break-even analysis withexample.

13. Explain capital investment analysis.

14. Explain different approaches to pricing andmethods of pricing.

15. Explain the regulations monopoly and restrictivetrade practices.

16. Explain the theory of income determination.

PART C (20 marks)

Compulsory

17. A company utilizing 55% of its installed capacitypurchases 6000 units of the raw material at Rs. 42per unit. The material and labour cost involved in

producing the raw material are Rs. 13 and Rs. 26respectively.


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(a) If installation of new facility require

Rs. 20,000

(i) Make a decision on make or buy

(ii) Find out the break even point

(iii)Calculate p/v ratio(iv) Calculate profit.

(b) If the unutilized capacity can be used with a

modification at a cost of Rs. 12,000

(i) Make a decision on make or buy

(ii) Find out the break even point

(iii) Calculate p/v ratio

(iv) Calculate profit.


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PMBC/PMB1C





1. Write a short note on social approach

2. Explain the classification and hierarchy of needs

as given by Maslow.

3. What do you mean by Locus of control?

4. Discuss the essential elements of communication

process.

5. Explain the approaches of leadership.

6. What are the different bases of power? Explain in

brief.

7. Discuss the importance in an organisational

climate.

8. List out the types of change. Explain them in

detail.


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9. Explain in brief the fundamental concepts of

Organizational Behaviour.

10. Group cohesiveness of high order leads to higher

group productivity Do you agree or disagree?

Explain.

11. Briefly discuss the types of incentives in

motivation.

12. Write a comprehensive note on barriers to

communication.

13. Explain in detail some of the methodologies for

managing political behaviour.

14. Briefly discuss the causes of stress.

15. What do you mean by OD interventions? Describe

the various OD interventions.

16. What are the outcomes of conflicts? How are the

conflicts managed?


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PART C (20 marks)

(Compulsory)

17. The T Aerospace Company is in the early stages of

planning the development of its latest commercial

jet, the 007. The aircraft industry is a fiercely

competitive one, dominated by a few large global

players who operate at the forefront of technology.

In this industry, competitors quickly copy and

advance in technology or new management

technique that might provide them with

competitive edge. Some of the T Aerospace

Companys competitors have adopted team

working as means of speeding up their

development and production processes.

The T Aerospace Company is thus considering the

adoption of team working in its operations but

some of the traditionalists in the company are

doubtful. They are concerned that the benefits of

work specialisation will be lost. Some of the

managers have negative experiences with team

working and so have strong reservations about the

proposed changes.


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Questions:

(a) List the four key components involved in

making an effective team.

(b) Identify the benefits that the T Aerospace

Company can expect to gain from the

adoption of team working.

(c) Describe the difficulties that the company is

likely to encounter in the management of its

teams and recommend ways to turn

individuals into team players.


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OCTOBER 2011 P/ID 77502/PMBB/

PMB1B





1. Define conditional probability. Illustrate it with an

example.

2. Distinguish between risk and uncertainty with

suitable examples.

3. Distinguish between regression and correlation.

4. What is factor rotation? Explain its necessity.

5. Distinguish between consumer surplus and

producer surplus.

6. List and explain the guidelines to preparebibliography.

(6 pages)


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7. Explain profile graph in cluster analysis with a

suitable example.

8. What are the types of hypothesis? Explain them

with examples.

PART B (5 10 = 50 marks)Answer any FIVE questions.


9. List and explain the approaches to probability.

10. A retail store desires to determine the optimal

daily order size for a perishable item. The stores

buys the perishable item at the rate of Rs. 60 per

kg and sells at the rate of Rs. 90 per kg. If the

order size is more than the demand. The excess

quantity can be sold at Rs. 75 per kg in a

secondary market. Otherwise, the opportunity cost

for the store is Rs. 10 per kg for the unsatisfied

portion of the demand. Based on the past

experience, it is found that the demand varies

from 50 kg to 200 kg in steps of 50 kg. The

possible values of the order size are from 100 kg to

300 kg in steps of 100 kg. Determine the optimal

order size which will maximize the daily profit of

the store using (a) Laplace criterion (b) Maximin

criterion.


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11. A placement agency has conducted a competitive

examination to create a potential database of

applicants for the post of Quality Manager for

their future recruitment. The classifications of the

applicants who secured more than 80 percentile in

the competitive examination are given below :

Check whether the present monthly salary is

independent of the number of years of experience

while grouping the applicants at a significance

level of 0.05.

Summary of data of applicants

Present monthly salary

(S)

No. of years of experience

(n)

(in thousands of Rs.) n < 2 2 < n < 5 5 < n

S< 10 40 35 30

10 < S< 14 30 20 35

14 < S< 18 30 30 40

18 < S 35 40 35

12. Alpha Industries Limited has deputed four

different batches of its employees to four differenttraining organizations (A, B, C and D) for the


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same training programme which aims to train

them in improving their decision making skills.

Each batch consists of five employees with similar

qualifications and work experience. After the

training programme, the company conducted a

common examination to test their level of

additional knowledge gained through the training

programme. The percentage scores of the

employees of the batches are summarized below :

Percentage scores of employees of batches in the

examination training organization

A B C D

80 70 65 90

90 60 50 89

96 55 58 85

85 85 55 95

70 90 40 80

Perform ANOVA to check whether there is

significant difference between the training

organizations in terms improving the decision

making skills of the employees by assuming a

significance level of 0.05.

[P.T.O.]


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13. What are the approaches of conjoint analysis?

Explain the steps of any one of them.

14. Suppose a manufacturer can sell xitems per week

at a price, xP 005.030 = rupee each when it

costs, 10004 += xy rupees to produce x items.

Determine the number of items he should produce

per week for maximum profit.

15. What are the types of report? Explain them in

brief.

16. The results of a survey on the sales of a product(Y)

as a function of time period (X) are summarized

below :

X Y

Mean 40 125

Standard deviation 2.5 16

Correlation coefficient (r) 0.85

(a) Fit the regression line of YonXand estimate

the value of YwhenXis 45

(b) Fit the regression line ofXon Yand estimate

the value ofXwhen Yis 135.


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PART C (20 marks)

(Compulsory)

17. A District Industries Center (DIC) has collected

data summarizing the number of industries in thedistrict under each combination of R & D

expenditure (in lakhs of rupees) and annual sales

(in crores of rupees) as shown below. Find the

correlation coefficient of this grouped data.

R & D Expenditure (in lakhs of rupees)

Annual sales 1030 3050 5070

(Crores of Rs.)

10 to 15 3 6 2

15 to 20 6 8 3

20 to 25 4 8 9

25 to 30 2 4 7

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Mathematics Model

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