# Download GTU MBA 2015 Winter 2nd Sem 2820007 Quantitative Analysis Ii Question Paper

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
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
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
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

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
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

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
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

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
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
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

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
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?