Download GTU (Gujarat Technological University) MBA (Master of Business Administration) 2015 Winter 2nd Sem 2820007 Quantitative Analysis Ii Previous Question Paper

GUJARAT TECHNOLOGICAL UNIVERSITY

MBA ? SEMESTER 02? ? EXAMINATION ? WINTER 2015

Subject Code: 2820007 Date: 23/12/2015

Subject Name: Quantitative Analysis - II

Time: 02.30 PM TO 05.30 PM Total Marks: 70

Instructions:

1. Attempt all questions.

2. Make suitable assumptions wherever necessary.

3. Figures to the right indicate full marks.

Q.1 A Identify the correct option and give the answer from the following questions. 6

1 When using a graphical solution procedure the region bounded by the set of constraint is called

the...

A Solution C Infeasible region

B Feasible region D Maximum profit

2 In the optimal solution to linear program, there are 20 units of slack for constraints. From this we

interpret that..

A The dual price for this constraint

is 20

C The dual price for this constraint is zero

B This constraints must be

redundant

D The problem must be maximization

3 If the total demand is greater than total supply in a transportation problem then,

A The optimal solution will be

degenerate

C A dummy destination must be added

B A dummy source must be added D Both dummy source and dummy

destination must be added

4 Customers enters the waiting line at a cafeteria on first come first serve basis. The arrival rate

follows a poison distribution and service time follows an exponential distribution. If the average

number of arrivals is 6 per minute and average service rate of single server is 10 per minute,

what is the value of utilizations parameter?

A 0.6 C 1.67

B 0.90 D 0.25

5 In the matrix of transition probabilities,

A The sum of probability in each

column equals to 1

C The sum of probability in each row

equals to 1

B There must be one zero in each

row

D There must be one zero in each column

6 Goal Programing

A Requires only that you know

whether goal is direct profit

maximization or cost

minimization

C Is an algorithm with the goal of quicker

solution to integer programming

problem

B Allows us to have multiple goals

with priorities

D None of the above

Q.1 (b) Explain the meaning of the following terms: 04

FirstRanker.com - FirstRanker's Choice

Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

MBA ? SEMESTER 02? ? EXAMINATION ? WINTER 2015

Subject Code: 2820007 Date: 23/12/2015

Subject Name: Quantitative Analysis - II

Time: 02.30 PM TO 05.30 PM Total Marks: 70

Instructions:

1. Attempt all questions.

2. Make suitable assumptions wherever necessary.

3. Figures to the right indicate full marks.

Q.1 A Identify the correct option and give the answer from the following questions. 6

1 When using a graphical solution procedure the region bounded by the set of constraint is called

the...

A Solution C Infeasible region

B Feasible region D Maximum profit

2 In the optimal solution to linear program, there are 20 units of slack for constraints. From this we

interpret that..

A The dual price for this constraint

is 20

C The dual price for this constraint is zero

B This constraints must be

redundant

D The problem must be maximization

3 If the total demand is greater than total supply in a transportation problem then,

A The optimal solution will be

degenerate

C A dummy destination must be added

B A dummy source must be added D Both dummy source and dummy

destination must be added

4 Customers enters the waiting line at a cafeteria on first come first serve basis. The arrival rate

follows a poison distribution and service time follows an exponential distribution. If the average

number of arrivals is 6 per minute and average service rate of single server is 10 per minute,

what is the value of utilizations parameter?

A 0.6 C 1.67

B 0.90 D 0.25

5 In the matrix of transition probabilities,

A The sum of probability in each

column equals to 1

C The sum of probability in each row

equals to 1

B There must be one zero in each

row

D There must be one zero in each column

6 Goal Programing

A Requires only that you know

whether goal is direct profit

maximization or cost

minimization

C Is an algorithm with the goal of quicker

solution to integer programming

problem

B Allows us to have multiple goals

with priorities

D None of the above

Q.1 (b) Explain the meaning of the following terms: 04

1. Constraints

2. Degeneracy

3. Balking (Queuing system)

4. Unbalanced assignment problem

Q.1 (c)

What is operation research? Explain the application of operation research

in the current scenario in management.

04

Q.2 (a) Write the dual of the following linear programming problems:

1. Z max = 8X1 + 10X2 + 5X3

W.S.C.

X1-X3?4

2X1+4X2?12

3X1+2X2-X3?7

X1,X2,X3 ? 0

2. Z Min = X1-3X2-2X3

W.S.C.

3X1-X2+2X3?7

2X1-4X2?12

-4X1+3X2+8X3=10

X1,X2?0 X3 Unrestricted in sign

07

(b) A salesman has to visit five cities A,B,C,D and E. The distance (In

Hundred KM) between the five cities are as follows:

A B C D E

A ---- 4 10 14 2

B 12 ---- 6 16 4

C 16 14 ---- 8 14

D 23 8 14 ---- 10

E 2 6 4 16 -----

If the salesman starts from city A and has to be come back to city A

under the condition that traveling salesman should travel each city only

once. Which route should he select so that the total distance travelled by

him is minimized?

07

OR

FirstRanker.com - FirstRanker's Choice

Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

MBA ? SEMESTER 02? ? EXAMINATION ? WINTER 2015

Subject Code: 2820007 Date: 23/12/2015

Subject Name: Quantitative Analysis - II

Time: 02.30 PM TO 05.30 PM Total Marks: 70

Instructions:

1. Attempt all questions.

2. Make suitable assumptions wherever necessary.

3. Figures to the right indicate full marks.

Q.1 A Identify the correct option and give the answer from the following questions. 6

1 When using a graphical solution procedure the region bounded by the set of constraint is called

the...

A Solution C Infeasible region

B Feasible region D Maximum profit

2 In the optimal solution to linear program, there are 20 units of slack for constraints. From this we

interpret that..

A The dual price for this constraint

is 20

C The dual price for this constraint is zero

B This constraints must be

redundant

D The problem must be maximization

3 If the total demand is greater than total supply in a transportation problem then,

A The optimal solution will be

degenerate

C A dummy destination must be added

B A dummy source must be added D Both dummy source and dummy

destination must be added

4 Customers enters the waiting line at a cafeteria on first come first serve basis. The arrival rate

follows a poison distribution and service time follows an exponential distribution. If the average

number of arrivals is 6 per minute and average service rate of single server is 10 per minute,

what is the value of utilizations parameter?

A 0.6 C 1.67

B 0.90 D 0.25

5 In the matrix of transition probabilities,

A The sum of probability in each

column equals to 1

C The sum of probability in each row

equals to 1

B There must be one zero in each

row

D There must be one zero in each column

6 Goal Programing

A Requires only that you know

whether goal is direct profit

maximization or cost

minimization

C Is an algorithm with the goal of quicker

solution to integer programming

problem

B Allows us to have multiple goals

with priorities

D None of the above

Q.1 (b) Explain the meaning of the following terms: 04

1. Constraints

2. Degeneracy

3. Balking (Queuing system)

4. Unbalanced assignment problem

Q.1 (c)

What is operation research? Explain the application of operation research

in the current scenario in management.

04

Q.2 (a) Write the dual of the following linear programming problems:

1. Z max = 8X1 + 10X2 + 5X3

W.S.C.

X1-X3?4

2X1+4X2?12

3X1+2X2-X3?7

X1,X2,X3 ? 0

2. Z Min = X1-3X2-2X3

W.S.C.

3X1-X2+2X3?7

2X1-4X2?12

-4X1+3X2+8X3=10

X1,X2?0 X3 Unrestricted in sign

07

(b) A salesman has to visit five cities A,B,C,D and E. The distance (In

Hundred KM) between the five cities are as follows:

A B C D E

A ---- 4 10 14 2

B 12 ---- 6 16 4

C 16 14 ---- 8 14

D 23 8 14 ---- 10

E 2 6 4 16 -----

If the salesman starts from city A and has to be come back to city A

under the condition that traveling salesman should travel each city only

once. Which route should he select so that the total distance travelled by

him is minimized?

07

OR

(b) Mr Nanavati is a leading advocate of our country, he employs typists on

hourly piece-rate basis for daily work. There are five typist and their

charges and typing speed are different. As per the decision of Mr

Nanavati, only one job was given to typist and the typist was paid for full

hour, even if he worked for the fraction of an hour. Find the most

suitable task for each typist and least allocation of the following data

with Hungarian methods:

Typist Rate

per

Hour

Number of

pages typed

per hour

A 15 12

B 16 14

C 10 09

D 12 10

E 14 11

Job/Task Number of

Pages

P 100

Q 88

R 75

S 150

T 90

07

Q.3 (a) What is Integer programming? Explain the various types of integer

programming in detail.

07

(b)

Roshni Goenka, a leading entrepreneur of Gujarat recently purchased a

farm house and is planning to install water system connecting to various

part of farms. The location of facilities and distance between them are

given in the following diagram. Derive the least expensive way to

provide water to each facilities by using the minimum spanning tree

technique.

07

OR

Q.3 (a) Write a shirt note on:

i. Goal Programming

ii. Sensitivity analysis

07

(b) Customers for famous TGB bakery arrived randomly following poisson

process. The single salesman can attend customers at an average rate of

10 customers per hour the service time being distributed exponentially.

The mean arrival rate is 10 minutes per customers. Find the answers of

the following questions:

1. What is the probability of having four customers in a queue?

2. What is the average time spent by customers in the TGB bakery?

3. What is the expected number of customers waiting in a queue?

07

FirstRanker.com - FirstRanker's Choice

Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

MBA ? SEMESTER 02? ? EXAMINATION ? WINTER 2015

Subject Code: 2820007 Date: 23/12/2015

Subject Name: Quantitative Analysis - II

Time: 02.30 PM TO 05.30 PM Total Marks: 70

Instructions:

1. Attempt all questions.

2. Make suitable assumptions wherever necessary.

3. Figures to the right indicate full marks.

Q.1 A Identify the correct option and give the answer from the following questions. 6

1 When using a graphical solution procedure the region bounded by the set of constraint is called

the...

A Solution C Infeasible region

B Feasible region D Maximum profit

2 In the optimal solution to linear program, there are 20 units of slack for constraints. From this we

interpret that..

A The dual price for this constraint

is 20

C The dual price for this constraint is zero

B This constraints must be

redundant

D The problem must be maximization

3 If the total demand is greater than total supply in a transportation problem then,

A The optimal solution will be

degenerate

C A dummy destination must be added

B A dummy source must be added D Both dummy source and dummy

destination must be added

4 Customers enters the waiting line at a cafeteria on first come first serve basis. The arrival rate

follows a poison distribution and service time follows an exponential distribution. If the average

number of arrivals is 6 per minute and average service rate of single server is 10 per minute,

what is the value of utilizations parameter?

A 0.6 C 1.67

B 0.90 D 0.25

5 In the matrix of transition probabilities,

A The sum of probability in each

column equals to 1

C The sum of probability in each row

equals to 1

B There must be one zero in each

row

D There must be one zero in each column

6 Goal Programing

A Requires only that you know

whether goal is direct profit

maximization or cost

minimization

C Is an algorithm with the goal of quicker

solution to integer programming

problem

B Allows us to have multiple goals

with priorities

D None of the above

Q.1 (b) Explain the meaning of the following terms: 04

1. Constraints

2. Degeneracy

3. Balking (Queuing system)

4. Unbalanced assignment problem

Q.1 (c)

What is operation research? Explain the application of operation research

in the current scenario in management.

04

Q.2 (a) Write the dual of the following linear programming problems:

1. Z max = 8X1 + 10X2 + 5X3

W.S.C.

X1-X3?4

2X1+4X2?12

3X1+2X2-X3?7

X1,X2,X3 ? 0

2. Z Min = X1-3X2-2X3

W.S.C.

3X1-X2+2X3?7

2X1-4X2?12

-4X1+3X2+8X3=10

X1,X2?0 X3 Unrestricted in sign

07

(b) A salesman has to visit five cities A,B,C,D and E. The distance (In

Hundred KM) between the five cities are as follows:

A B C D E

A ---- 4 10 14 2

B 12 ---- 6 16 4

C 16 14 ---- 8 14

D 23 8 14 ---- 10

E 2 6 4 16 -----

If the salesman starts from city A and has to be come back to city A

under the condition that traveling salesman should travel each city only

once. Which route should he select so that the total distance travelled by

him is minimized?

07

OR

(b) Mr Nanavati is a leading advocate of our country, he employs typists on

hourly piece-rate basis for daily work. There are five typist and their

charges and typing speed are different. As per the decision of Mr

Nanavati, only one job was given to typist and the typist was paid for full

hour, even if he worked for the fraction of an hour. Find the most

suitable task for each typist and least allocation of the following data

with Hungarian methods:

Typist Rate

per

Hour

Number of

pages typed

per hour

A 15 12

B 16 14

C 10 09

D 12 10

E 14 11

Job/Task Number of

Pages

P 100

Q 88

R 75

S 150

T 90

07

Q.3 (a) What is Integer programming? Explain the various types of integer

programming in detail.

07

(b)

Roshni Goenka, a leading entrepreneur of Gujarat recently purchased a

farm house and is planning to install water system connecting to various

part of farms. The location of facilities and distance between them are

given in the following diagram. Derive the least expensive way to

provide water to each facilities by using the minimum spanning tree

technique.

07

OR

Q.3 (a) Write a shirt note on:

i. Goal Programming

ii. Sensitivity analysis

07

(b) Customers for famous TGB bakery arrived randomly following poisson

process. The single salesman can attend customers at an average rate of

10 customers per hour the service time being distributed exponentially.

The mean arrival rate is 10 minutes per customers. Find the answers of

the following questions:

1. What is the probability of having four customers in a queue?

2. What is the average time spent by customers in the TGB bakery?

3. What is the expected number of customers waiting in a queue?

07

4. What is the probability that the waiting time of customer in queue

shall be more than 15 minutes in bakery?

(e

-1

= 0.368, e

-2

= 0.1353)

Q.4 (a) Write a short note on,

1. Various types of queuing structure

2. Brand switching in Markov chain process

07

(b) Sales India, a leading consumer durables dealer stocks 1.5 tons Air

conditions that it sells to home owners and installs for them at free of

cost. The owner, Mr John, likes the idea of having large supply on hand

to meet the customer demand. At the same time he understands that it

is very expensive process. He examines the sale of ACs over past 100

weeks and notes the following:

ACs

sold per

week

22 23 24 25 26 27 28 29 30

Number

of

weeks

2 9 10 15 25 14 12 8 5

1. If Sales India maintains a constant supply of 26 AC in any given

week, how many times will they be out of the stock during 10

weeks simulations? You can use the following random numbers for

the calculations: (10,24,03,32,23,59,95,34,35,51)

2. What is the average number of sales per week (including the stock

outs) over the 10 weeks period?

3. Using an analytical non simulation technique, what is the expected

number of sales per week? How does this compare with the

simulation technique?

07

OR

Q.4 (a) What is Simulations? Explain the Monte Carlo method of simulation.

Also state the merits and the demerits of the same.

07

(b) In Gujarat, oral care market is very competitive and mainly two major

group dominate the market: Colgate and Pepsodent. It is given that a

customer last purchased brand Colgate 70 percent of chance that he

would buy the same brand in next purchase. While if a customer

purchases brand Pepsodent, there are 60 percent of chances that his next

purchase would be the same brand. Using this information develop the

transition probability matrix and answer the following questions:

1. Find the probability that customer currently is a brand Colgate

purchaser, he will purchase brand Pepsodent two purchases from

now.

2. Find the probability that a customer brand Pepsodent purchaser,

he will purchase brand Colgate three periods from now.

3. Also find steady state probability market share of two brands and

interpret the results.

07

Q.5 Recently Ford Limited launched new plant in Gujarat near Ahmedabad.

In the new plant of company, they produce two types of cars: Ford Figo

and Ford Fiesta. The production manager of the plant shares the

14

FirstRanker.com - FirstRanker's Choice

Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

MBA ? SEMESTER 02? ? EXAMINATION ? WINTER 2015

Subject Code: 2820007 Date: 23/12/2015

Subject Name: Quantitative Analysis - II

Time: 02.30 PM TO 05.30 PM Total Marks: 70

Instructions:

1. Attempt all questions.

2. Make suitable assumptions wherever necessary.

3. Figures to the right indicate full marks.

Q.1 A Identify the correct option and give the answer from the following questions. 6

1 When using a graphical solution procedure the region bounded by the set of constraint is called

the...

A Solution C Infeasible region

B Feasible region D Maximum profit

2 In the optimal solution to linear program, there are 20 units of slack for constraints. From this we

interpret that..

A The dual price for this constraint

is 20

C The dual price for this constraint is zero

B This constraints must be

redundant

D The problem must be maximization

3 If the total demand is greater than total supply in a transportation problem then,

A The optimal solution will be

degenerate

C A dummy destination must be added

B A dummy source must be added D Both dummy source and dummy

destination must be added

4 Customers enters the waiting line at a cafeteria on first come first serve basis. The arrival rate

follows a poison distribution and service time follows an exponential distribution. If the average

number of arrivals is 6 per minute and average service rate of single server is 10 per minute,

what is the value of utilizations parameter?

A 0.6 C 1.67

B 0.90 D 0.25

5 In the matrix of transition probabilities,

A The sum of probability in each

column equals to 1

C The sum of probability in each row

equals to 1

B There must be one zero in each

row

D There must be one zero in each column

6 Goal Programing

A Requires only that you know

whether goal is direct profit

maximization or cost

minimization

C Is an algorithm with the goal of quicker

solution to integer programming

problem

B Allows us to have multiple goals

with priorities

D None of the above

Q.1 (b) Explain the meaning of the following terms: 04

1. Constraints

2. Degeneracy

3. Balking (Queuing system)

4. Unbalanced assignment problem

Q.1 (c)

What is operation research? Explain the application of operation research

in the current scenario in management.

04

Q.2 (a) Write the dual of the following linear programming problems:

1. Z max = 8X1 + 10X2 + 5X3

W.S.C.

X1-X3?4

2X1+4X2?12

3X1+2X2-X3?7

X1,X2,X3 ? 0

2. Z Min = X1-3X2-2X3

W.S.C.

3X1-X2+2X3?7

2X1-4X2?12

-4X1+3X2+8X3=10

X1,X2?0 X3 Unrestricted in sign

07

(b) A salesman has to visit five cities A,B,C,D and E. The distance (In

Hundred KM) between the five cities are as follows:

A B C D E

A ---- 4 10 14 2

B 12 ---- 6 16 4

C 16 14 ---- 8 14

D 23 8 14 ---- 10

E 2 6 4 16 -----

If the salesman starts from city A and has to be come back to city A

under the condition that traveling salesman should travel each city only

once. Which route should he select so that the total distance travelled by

him is minimized?

07

OR

(b) Mr Nanavati is a leading advocate of our country, he employs typists on

hourly piece-rate basis for daily work. There are five typist and their

charges and typing speed are different. As per the decision of Mr

Nanavati, only one job was given to typist and the typist was paid for full

hour, even if he worked for the fraction of an hour. Find the most

suitable task for each typist and least allocation of the following data

with Hungarian methods:

Typist Rate

per

Hour

Number of

pages typed

per hour

A 15 12

B 16 14

C 10 09

D 12 10

E 14 11

Job/Task Number of

Pages

P 100

Q 88

R 75

S 150

T 90

07

Q.3 (a) What is Integer programming? Explain the various types of integer

programming in detail.

07

(b)

Roshni Goenka, a leading entrepreneur of Gujarat recently purchased a

farm house and is planning to install water system connecting to various

part of farms. The location of facilities and distance between them are

given in the following diagram. Derive the least expensive way to

provide water to each facilities by using the minimum spanning tree

technique.

07

OR

Q.3 (a) Write a shirt note on:

i. Goal Programming

ii. Sensitivity analysis

07

(b) Customers for famous TGB bakery arrived randomly following poisson

process. The single salesman can attend customers at an average rate of

10 customers per hour the service time being distributed exponentially.

The mean arrival rate is 10 minutes per customers. Find the answers of

the following questions:

1. What is the probability of having four customers in a queue?

2. What is the average time spent by customers in the TGB bakery?

3. What is the expected number of customers waiting in a queue?

07

4. What is the probability that the waiting time of customer in queue

shall be more than 15 minutes in bakery?

(e

-1

= 0.368, e

-2

= 0.1353)

Q.4 (a) Write a short note on,

1. Various types of queuing structure

2. Brand switching in Markov chain process

07

(b) Sales India, a leading consumer durables dealer stocks 1.5 tons Air

conditions that it sells to home owners and installs for them at free of

cost. The owner, Mr John, likes the idea of having large supply on hand

to meet the customer demand. At the same time he understands that it

is very expensive process. He examines the sale of ACs over past 100

weeks and notes the following:

ACs

sold per

week

22 23 24 25 26 27 28 29 30

Number

of

weeks

2 9 10 15 25 14 12 8 5

1. If Sales India maintains a constant supply of 26 AC in any given

week, how many times will they be out of the stock during 10

weeks simulations? You can use the following random numbers for

the calculations: (10,24,03,32,23,59,95,34,35,51)

2. What is the average number of sales per week (including the stock

outs) over the 10 weeks period?

3. Using an analytical non simulation technique, what is the expected

number of sales per week? How does this compare with the

simulation technique?

07

OR

Q.4 (a) What is Simulations? Explain the Monte Carlo method of simulation.

Also state the merits and the demerits of the same.

07

(b) In Gujarat, oral care market is very competitive and mainly two major

group dominate the market: Colgate and Pepsodent. It is given that a

customer last purchased brand Colgate 70 percent of chance that he

would buy the same brand in next purchase. While if a customer

purchases brand Pepsodent, there are 60 percent of chances that his next

purchase would be the same brand. Using this information develop the

transition probability matrix and answer the following questions:

1. Find the probability that customer currently is a brand Colgate

purchaser, he will purchase brand Pepsodent two purchases from

now.

2. Find the probability that a customer brand Pepsodent purchaser,

he will purchase brand Colgate three periods from now.

3. Also find steady state probability market share of two brands and

interpret the results.

07

Q.5 Recently Ford Limited launched new plant in Gujarat near Ahmedabad.

In the new plant of company, they produce two types of cars: Ford Figo

and Ford Fiesta. The production manager of the plant shares the

14

following information regarding the worker/technocrat, assembly time

and finishing time for Figo and Fiesta.

Worker/technocrat Assembly time Finishing time

Figo 12 3 8

Fiesta 12 6 4

In this plant of Ford, currently 840 Worker/technocrat provide the service

and not more than 300 hours of assembly time and 480 hours of the

finishing time available. CEO of Ford Ltd is confident about profit of

new Figo 50,000 Rs and Fiesta 70,000 Rs. On the basis of the given

information formulate the LPP and solve by graphical methods. Give the

answer of the following questions with suitable quantitative tools:

1. Derive the binding and non binding constraints of the problems

and interpret each of them.

2. How much would the cost increase if 1000 workers are rendered

by the company instead of 840? And with the special effort

assembly time were increased from 300 hours to 400 hours, what

will be the implications?

3. The production manager of Ford Ltd want to start a

manufacturing Ecosport car in the same plant, to manufacture this

car require 15 workers, 8 hours of assembly time and 10 hours of

finishing time. Ecosport generates the profit of 85,000 Rs. Being

the consultant of the company give your valuable advice to the

production manager with suitable justification, whether the

company should start manufacturing Ecosports car in the same

plant or not?

4.

OR

Q.5 ABG shipping corp. is a leading shipping corporation of the nation. They

have offices in Mumbai and Gandhidham. They provide services to

different company and transport their goods to warehouses to

marketplaces. The following table provides all necessary information on

the availability of supply of each warehouse to the requirement of the

various markets. And the unit transportation cost in thousand Rs from

each warehouse to each market is mentioned below.

Markets

Warehouse P Q R S Supply

A 6 3 5 4 22

B 5 9 2 7 15

C 5 7 8 6 8

Demand 7 12 17 9 45

Mr Sanjay, the shipping clerk of ABG shipping agency usually prepares

schedule of transportation based on his expertise and vast experience. Mr

Sanjay has worked out the following schedule on the basis of

assumptions.

1. 12 units from A to Q

14

FirstRanker.com - FirstRanker's Choice

Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

MBA ? SEMESTER 02? ? EXAMINATION ? WINTER 2015

Subject Code: 2820007 Date: 23/12/2015

Subject Name: Quantitative Analysis - II

Time: 02.30 PM TO 05.30 PM Total Marks: 70

Instructions:

1. Attempt all questions.

2. Make suitable assumptions wherever necessary.

3. Figures to the right indicate full marks.

Q.1 A Identify the correct option and give the answer from the following questions. 6

1 When using a graphical solution procedure the region bounded by the set of constraint is called

the...

A Solution C Infeasible region

B Feasible region D Maximum profit

2 In the optimal solution to linear program, there are 20 units of slack for constraints. From this we

interpret that..

A The dual price for this constraint

is 20

C The dual price for this constraint is zero

B This constraints must be

redundant

D The problem must be maximization

3 If the total demand is greater than total supply in a transportation problem then,

A The optimal solution will be

degenerate

C A dummy destination must be added

B A dummy source must be added D Both dummy source and dummy

destination must be added

4 Customers enters the waiting line at a cafeteria on first come first serve basis. The arrival rate

follows a poison distribution and service time follows an exponential distribution. If the average

number of arrivals is 6 per minute and average service rate of single server is 10 per minute,

what is the value of utilizations parameter?

A 0.6 C 1.67

B 0.90 D 0.25

5 In the matrix of transition probabilities,

A The sum of probability in each

column equals to 1

C The sum of probability in each row

equals to 1

B There must be one zero in each

row

D There must be one zero in each column

6 Goal Programing

A Requires only that you know

whether goal is direct profit

maximization or cost

minimization

C Is an algorithm with the goal of quicker

solution to integer programming

problem

B Allows us to have multiple goals

with priorities

D None of the above

Q.1 (b) Explain the meaning of the following terms: 04

1. Constraints

2. Degeneracy

3. Balking (Queuing system)

4. Unbalanced assignment problem

Q.1 (c)

What is operation research? Explain the application of operation research

in the current scenario in management.

04

Q.2 (a) Write the dual of the following linear programming problems:

1. Z max = 8X1 + 10X2 + 5X3

W.S.C.

X1-X3?4

2X1+4X2?12

3X1+2X2-X3?7

X1,X2,X3 ? 0

2. Z Min = X1-3X2-2X3

W.S.C.

3X1-X2+2X3?7

2X1-4X2?12

-4X1+3X2+8X3=10

X1,X2?0 X3 Unrestricted in sign

07

(b) A salesman has to visit five cities A,B,C,D and E. The distance (In

Hundred KM) between the five cities are as follows:

A B C D E

A ---- 4 10 14 2

B 12 ---- 6 16 4

C 16 14 ---- 8 14

D 23 8 14 ---- 10

E 2 6 4 16 -----

If the salesman starts from city A and has to be come back to city A

under the condition that traveling salesman should travel each city only

once. Which route should he select so that the total distance travelled by

him is minimized?

07

OR

(b) Mr Nanavati is a leading advocate of our country, he employs typists on

hourly piece-rate basis for daily work. There are five typist and their

charges and typing speed are different. As per the decision of Mr

Nanavati, only one job was given to typist and the typist was paid for full

hour, even if he worked for the fraction of an hour. Find the most

suitable task for each typist and least allocation of the following data

with Hungarian methods:

Typist Rate

per

Hour

Number of

pages typed

per hour

A 15 12

B 16 14

C 10 09

D 12 10

E 14 11

Job/Task Number of

Pages

P 100

Q 88

R 75

S 150

T 90

07

Q.3 (a) What is Integer programming? Explain the various types of integer

programming in detail.

07

(b)

Roshni Goenka, a leading entrepreneur of Gujarat recently purchased a

farm house and is planning to install water system connecting to various

part of farms. The location of facilities and distance between them are

given in the following diagram. Derive the least expensive way to

provide water to each facilities by using the minimum spanning tree

technique.

07

OR

Q.3 (a) Write a shirt note on:

i. Goal Programming

ii. Sensitivity analysis

07

(b) Customers for famous TGB bakery arrived randomly following poisson

process. The single salesman can attend customers at an average rate of

10 customers per hour the service time being distributed exponentially.

The mean arrival rate is 10 minutes per customers. Find the answers of

the following questions:

1. What is the probability of having four customers in a queue?

2. What is the average time spent by customers in the TGB bakery?

3. What is the expected number of customers waiting in a queue?

07

4. What is the probability that the waiting time of customer in queue

shall be more than 15 minutes in bakery?

(e

-1

= 0.368, e

-2

= 0.1353)

Q.4 (a) Write a short note on,

1. Various types of queuing structure

2. Brand switching in Markov chain process

07

(b) Sales India, a leading consumer durables dealer stocks 1.5 tons Air

conditions that it sells to home owners and installs for them at free of

cost. The owner, Mr John, likes the idea of having large supply on hand

to meet the customer demand. At the same time he understands that it

is very expensive process. He examines the sale of ACs over past 100

weeks and notes the following:

ACs

sold per

week

22 23 24 25 26 27 28 29 30

Number

of

weeks

2 9 10 15 25 14 12 8 5

1. If Sales India maintains a constant supply of 26 AC in any given

week, how many times will they be out of the stock during 10

weeks simulations? You can use the following random numbers for

the calculations: (10,24,03,32,23,59,95,34,35,51)

2. What is the average number of sales per week (including the stock

outs) over the 10 weeks period?

3. Using an analytical non simulation technique, what is the expected

number of sales per week? How does this compare with the

simulation technique?

07

OR

Q.4 (a) What is Simulations? Explain the Monte Carlo method of simulation.

Also state the merits and the demerits of the same.

07

(b) In Gujarat, oral care market is very competitive and mainly two major

group dominate the market: Colgate and Pepsodent. It is given that a

customer last purchased brand Colgate 70 percent of chance that he

would buy the same brand in next purchase. While if a customer

purchases brand Pepsodent, there are 60 percent of chances that his next

purchase would be the same brand. Using this information develop the

transition probability matrix and answer the following questions:

1. Find the probability that customer currently is a brand Colgate

purchaser, he will purchase brand Pepsodent two purchases from

now.

2. Find the probability that a customer brand Pepsodent purchaser,

he will purchase brand Colgate three periods from now.

3. Also find steady state probability market share of two brands and

interpret the results.

07

Q.5 Recently Ford Limited launched new plant in Gujarat near Ahmedabad.

In the new plant of company, they produce two types of cars: Ford Figo

and Ford Fiesta. The production manager of the plant shares the

14

following information regarding the worker/technocrat, assembly time

and finishing time for Figo and Fiesta.

Worker/technocrat Assembly time Finishing time

Figo 12 3 8

Fiesta 12 6 4

In this plant of Ford, currently 840 Worker/technocrat provide the service

and not more than 300 hours of assembly time and 480 hours of the

finishing time available. CEO of Ford Ltd is confident about profit of

new Figo 50,000 Rs and Fiesta 70,000 Rs. On the basis of the given

information formulate the LPP and solve by graphical methods. Give the

answer of the following questions with suitable quantitative tools:

1. Derive the binding and non binding constraints of the problems

and interpret each of them.

2. How much would the cost increase if 1000 workers are rendered

by the company instead of 840? And with the special effort

assembly time were increased from 300 hours to 400 hours, what

will be the implications?

3. The production manager of Ford Ltd want to start a

manufacturing Ecosport car in the same plant, to manufacture this

car require 15 workers, 8 hours of assembly time and 10 hours of

finishing time. Ecosport generates the profit of 85,000 Rs. Being

the consultant of the company give your valuable advice to the

production manager with suitable justification, whether the

company should start manufacturing Ecosports car in the same

plant or not?

4.

OR

Q.5 ABG shipping corp. is a leading shipping corporation of the nation. They

have offices in Mumbai and Gandhidham. They provide services to

different company and transport their goods to warehouses to

marketplaces. The following table provides all necessary information on

the availability of supply of each warehouse to the requirement of the

various markets. And the unit transportation cost in thousand Rs from

each warehouse to each market is mentioned below.

Markets

Warehouse P Q R S Supply

A 6 3 5 4 22

B 5 9 2 7 15

C 5 7 8 6 8

Demand 7 12 17 9 45

Mr Sanjay, the shipping clerk of ABG shipping agency usually prepares

schedule of transportation based on his expertise and vast experience. Mr

Sanjay has worked out the following schedule on the basis of

assumptions.

1. 12 units from A to Q

14

2. 1 unit from A to R

3. 9 units from A to S

4. 15 units from B to R

5. 7 units from C to P

6. 1 unit from C to R

1. Being a consultant of the company, check and analyze wether Mr

Sanjay has arranged optimal schedule or not? You can apply

transportation method.

2. Find the optimal schedule and minimum total transportation cost

whether this problem has only one optimal solution or not?

Justify your answer.

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This post was last modified on 19 February 2020