# Download GTU MBA 2016 Summer 2nd Sem 2820007 Quantitative Analysis Ii Qa Ii Question Paper

Download GTU (Gujarat Technological University) MBA (Master of Business Administration) 2016 Summer 2nd Sem 2820007 Quantitative Analysis Ii Qa Ii Previous Question Paper

Page 1 of 4

Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY
MBA ? SEMESTER 02? ? EXAMINATION ? SUMMER 2016

Subject Code: 2820007 Date: 20/05/2016
Subject Name: QUANTITATIVE ANALYSIS-II (QA-II)
Time: 10.30 AM TO 01.30 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 06
1. If the number of filled cells in a transportation table does not equal the number of rows
plus the number of columns minus 1, then the problem is said to be
A. unbalanced B degenerate
C. optimal D maximization problem
2. A typical transportation problem has 4 sources and 3 destinations. How many
constraints would there be in the linear program for this?
A. 3 B 4
C. 7 D 12
3. An LP problem has a bounded feasible region. If this problem has an equality (=)
constraint, then
A. this must be a minimization problem B the feasible region must consist
of a line segment.
C. the problem must be degenerate D the problem must have more
than one optimal solution.
4. If a transportation problem has 4 sources and 5 destinations, the linear program for this
will have
A. 4 variables and 5 constraints B 5 variable and 4 constraints
C. 9 variables and 20 constraints D 20 variables and 9 constraints
5. When simulating the Monte Carlo experiment, the average simulated demand over the
long run should approximate the
A. real demand B expected demand
C. sample demand D Daily demand.
6. A company has one computer technician who is responsible for repairs on the
company?s 20 computers. As a computer breaks, the technician is called to make the
repair. If the repairperson is busy, the machine must wait to be repaired. This is an
example of
A. a multichannel system B a finite population system
C. a constant service rate system D a multiphase system

Q.1 (b) Define following: 1) Shadow Prices; 2) Unboundedness; 3) Binary
variables; 4) Global optimum
04

Q.1 (c) Write differences between Assignment Problem Vs Travelling salesman
Problem
04

Q.2 (a) Explain the concept of duality with suitable examples. 07
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Page 1 of 4

Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY
MBA ? SEMESTER 02? ? EXAMINATION ? SUMMER 2016

Subject Code: 2820007 Date: 20/05/2016
Subject Name: QUANTITATIVE ANALYSIS-II (QA-II)
Time: 10.30 AM TO 01.30 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 06
1. If the number of filled cells in a transportation table does not equal the number of rows
plus the number of columns minus 1, then the problem is said to be
A. unbalanced B degenerate
C. optimal D maximization problem
2. A typical transportation problem has 4 sources and 3 destinations. How many
constraints would there be in the linear program for this?
A. 3 B 4
C. 7 D 12
3. An LP problem has a bounded feasible region. If this problem has an equality (=)
constraint, then
A. this must be a minimization problem B the feasible region must consist
of a line segment.
C. the problem must be degenerate D the problem must have more
than one optimal solution.
4. If a transportation problem has 4 sources and 5 destinations, the linear program for this
will have
A. 4 variables and 5 constraints B 5 variable and 4 constraints
C. 9 variables and 20 constraints D 20 variables and 9 constraints
5. When simulating the Monte Carlo experiment, the average simulated demand over the
long run should approximate the
A. real demand B expected demand
C. sample demand D Daily demand.
6. A company has one computer technician who is responsible for repairs on the
company?s 20 computers. As a computer breaks, the technician is called to make the
repair. If the repairperson is busy, the machine must wait to be repaired. This is an
example of
A. a multichannel system B a finite population system
C. a constant service rate system D a multiphase system

Q.1 (b) Define following: 1) Shadow Prices; 2) Unboundedness; 3) Binary
variables; 4) Global optimum
04

Q.1 (c) Write differences between Assignment Problem Vs Travelling salesman
Problem
04

Q.2 (a) Explain the concept of duality with suitable examples. 07
Page 2 of 4

(b) India Inc., manufactures two products used in the heavy equipment
industry. Both products require manufacturing operations in two
departments. The following are the production time(in hours) and profit
contribution figures for the two products:
Labour Hours
Product Profit per Unit Dept. A Dept. B
1 Rs. 25 6 12
2 Rs. 20 8 10
For the coming production period, India Inc., has available a total of 900
hours of labour that can be allocated to either of the two departments.
Formulate the LPP

07
OR
(b) With a view to improving the quality of customer services, a bank is
interested in making an ?assessment of the waiting time of its customers?
coming to one of its branches located in a residential area. This branch has
only one tellers? counter. The arrival rate of the customers and the service
rate of the teller are given below:
Time Between two consecutive
arrivals of customers
( In minutes)
Probability Service time
by the teller
( In minutes)
Probability
3 0.17 3 0.10
4 0.25 4 0.30
5 0.25 5 0.40
6 0.20 6 0.15
7 0.13 7 0.05
Total 1.00 Total 1.00
You are required to simulate 10 arrivals of customers in the system starting
from 11 AM and show the waiting time of the customers and idle time of
the teller in the analysis table. Use of the following random numbers taking
the pair of random numbers in two digits each for first trial and so on:
(11,56), (23,72), (94,83), (83,02), (97, 99), (83,10), (93,34), (33,53),
(49,94), (37,77); where first random number in the bracket is for arrival and
second random number is for service. Compute probability that the teller is
idle. Hence, determine average inter-arrival time (min) and average
services time (min) using simulation technique. Also determine average.
waiting time of the customers before getting the service and average time
spent by a customer in the bank.
07

Q.3 (a) Explain the concepts of single server queuing model specified by
(M/M/1): (?/FIFO)
07
(b) Geraldine Shawhan is president of Shawhan File Works, a firm that
manufactures two types of metal file cabinets. The demand for her two-
drawer model is up to 600 cabinets per week; demand for a three drawer
cabinet is limited to 400 per week. Shawhan File Works has a weekly
operating capacity of 1,300 hours, with the two-drawer cabinet taking 1
hour to produce and the three-drawer cabinet requiring 2 hours. Each two-
drawer model sold yields a \$10 profit, and the profit for the large model is
\$15. Shawhan has listed the following goals in order of importance:
1. Attain a profit as close to \$11,000 as possible each week.
2. Avoid underutilization of the firm?s production capacity.
3. Sell as many two- and three-drawer cabinets as the demand indicates.
Set this up as a goal programming problem.
07
OR
Q.3 (a) A tailor specializes in ladies? dresses. The number of customers
approaching to the tailor appears to be Poisson distributed with mean of 6
customers per hour. The tailor attends the customers on first come first
serve basis and the customers wait if the need be. The tailor can attend the
07
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Page 1 of 4

Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY
MBA ? SEMESTER 02? ? EXAMINATION ? SUMMER 2016

Subject Code: 2820007 Date: 20/05/2016
Subject Name: QUANTITATIVE ANALYSIS-II (QA-II)
Time: 10.30 AM TO 01.30 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 06
1. If the number of filled cells in a transportation table does not equal the number of rows
plus the number of columns minus 1, then the problem is said to be
A. unbalanced B degenerate
C. optimal D maximization problem
2. A typical transportation problem has 4 sources and 3 destinations. How many
constraints would there be in the linear program for this?
A. 3 B 4
C. 7 D 12
3. An LP problem has a bounded feasible region. If this problem has an equality (=)
constraint, then
A. this must be a minimization problem B the feasible region must consist
of a line segment.
C. the problem must be degenerate D the problem must have more
than one optimal solution.
4. If a transportation problem has 4 sources and 5 destinations, the linear program for this
will have
A. 4 variables and 5 constraints B 5 variable and 4 constraints
C. 9 variables and 20 constraints D 20 variables and 9 constraints
5. When simulating the Monte Carlo experiment, the average simulated demand over the
long run should approximate the
A. real demand B expected demand
C. sample demand D Daily demand.
6. A company has one computer technician who is responsible for repairs on the
company?s 20 computers. As a computer breaks, the technician is called to make the
repair. If the repairperson is busy, the machine must wait to be repaired. This is an
example of
A. a multichannel system B a finite population system
C. a constant service rate system D a multiphase system

Q.1 (b) Define following: 1) Shadow Prices; 2) Unboundedness; 3) Binary
variables; 4) Global optimum
04

Q.1 (c) Write differences between Assignment Problem Vs Travelling salesman
Problem
04

Q.2 (a) Explain the concept of duality with suitable examples. 07
Page 2 of 4

(b) India Inc., manufactures two products used in the heavy equipment
industry. Both products require manufacturing operations in two
departments. The following are the production time(in hours) and profit
contribution figures for the two products:
Labour Hours
Product Profit per Unit Dept. A Dept. B
1 Rs. 25 6 12
2 Rs. 20 8 10
For the coming production period, India Inc., has available a total of 900
hours of labour that can be allocated to either of the two departments.
Formulate the LPP

07
OR
(b) With a view to improving the quality of customer services, a bank is
interested in making an ?assessment of the waiting time of its customers?
coming to one of its branches located in a residential area. This branch has
only one tellers? counter. The arrival rate of the customers and the service
rate of the teller are given below:
Time Between two consecutive
arrivals of customers
( In minutes)
Probability Service time
by the teller
( In minutes)
Probability
3 0.17 3 0.10
4 0.25 4 0.30
5 0.25 5 0.40
6 0.20 6 0.15
7 0.13 7 0.05
Total 1.00 Total 1.00
You are required to simulate 10 arrivals of customers in the system starting
from 11 AM and show the waiting time of the customers and idle time of
the teller in the analysis table. Use of the following random numbers taking
the pair of random numbers in two digits each for first trial and so on:
(11,56), (23,72), (94,83), (83,02), (97, 99), (83,10), (93,34), (33,53),
(49,94), (37,77); where first random number in the bracket is for arrival and
second random number is for service. Compute probability that the teller is
idle. Hence, determine average inter-arrival time (min) and average
services time (min) using simulation technique. Also determine average.
waiting time of the customers before getting the service and average time
spent by a customer in the bank.
07

Q.3 (a) Explain the concepts of single server queuing model specified by
(M/M/1): (?/FIFO)
07
(b) Geraldine Shawhan is president of Shawhan File Works, a firm that
manufactures two types of metal file cabinets. The demand for her two-
drawer model is up to 600 cabinets per week; demand for a three drawer
cabinet is limited to 400 per week. Shawhan File Works has a weekly
operating capacity of 1,300 hours, with the two-drawer cabinet taking 1
hour to produce and the three-drawer cabinet requiring 2 hours. Each two-
drawer model sold yields a \$10 profit, and the profit for the large model is
\$15. Shawhan has listed the following goals in order of importance:
1. Attain a profit as close to \$11,000 as possible each week.
2. Avoid underutilization of the firm?s production capacity.
3. Sell as many two- and three-drawer cabinets as the demand indicates.
Set this up as a goal programming problem.
07
OR
Q.3 (a) A tailor specializes in ladies? dresses. The number of customers
approaching to the tailor appears to be Poisson distributed with mean of 6
customers per hour. The tailor attends the customers on first come first
serve basis and the customers wait if the need be. The tailor can attend the
07
Page 3 of 4

customers at an average rate of 10 per hour with the service time be
exponentially distributed. Find (i) the utilization factor, (ii) probability that
the system is idle, (iii) the average time that the tailor is free on a 10-hour
working day, (iv) the probability associated with the number of customers;
0 through 3, in the system, (v) expected (average) number of customers in
the shop & expected number of customers waiting for tailor?s service, (vi)
how much time a customer expect to spend in the queue and in the shop?
(vii) Probability that there are more than 3 customers in the shop.
(b) Consider the following LP: Min 2A+2B stc 1A + 3B ? 12; 3A+1B ?13;
1A-1B = 3 and A,B?0. i) Show the feasible region; ii) What are the extreme
points of the feasible region; iii) Find the optimal solution using the
graphical solution procedure
07

Q.4 (a) Compare the similarities and differences of linear and goal programming. 07
(b) A repairman is to be hired by a company to repair machines that
breakdown. Number of breakdown follows Poisson distribution with an
average rate of four per hour. The cost of non-productive machine time is
Rs. 90 per hour. The company has the option of choosing either a fast or a
slow repairman. The fast repairman charges Rs. 70 per hour and will repair
machines at an average rate of 7 machines per hour, while the slow
repairman charges Rs. 50 per hour and will repair at the rate of 6 per hour.
Determine who should be hired.
07
OR
(b) Grey Construction would like to determine the least expensive way of
connecting houses it is building with cable TV. It has identified 11 possible
branches or routes that could be used to connect the houses. The cost in
hundreds of dollars and the branches are summarized in the following table.
What is the least expensive way to run cable to the houses?
Branch Start Node End Node Cost(\$100s)
Branch 1 1 2 5
Branch 2 1 3 6
Branch 3 1 4 6
Branch 4 1 5 5
Branch 5 2 6 7
Branch 6 3 7 5
Branch 7 4 7 7
Branch 8 5 8 4
Branch 9 6 7 1
Branch 10 7 9 6
Branch 11 8 9 2

07

Q.5 XYZ tobacco company purchases and stores in warehouses located in
following four cities:
Warehouse A B C D
Capacity (tones) 90 50 80 60
The warehouses supply tobacco cigarette companies in three cities that have
the following demand:
Cigarette Company Bharat Janta Red Lamp
Demand (tones) 120 100 110
The following railroad shipping costs (in hundred rupees) per ton have been
determined:

14
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Page 1 of 4

Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY
MBA ? SEMESTER 02? ? EXAMINATION ? SUMMER 2016

Subject Code: 2820007 Date: 20/05/2016
Subject Name: QUANTITATIVE ANALYSIS-II (QA-II)
Time: 10.30 AM TO 01.30 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 06
1. If the number of filled cells in a transportation table does not equal the number of rows
plus the number of columns minus 1, then the problem is said to be
A. unbalanced B degenerate
C. optimal D maximization problem
2. A typical transportation problem has 4 sources and 3 destinations. How many
constraints would there be in the linear program for this?
A. 3 B 4
C. 7 D 12
3. An LP problem has a bounded feasible region. If this problem has an equality (=)
constraint, then
A. this must be a minimization problem B the feasible region must consist
of a line segment.
C. the problem must be degenerate D the problem must have more
than one optimal solution.
4. If a transportation problem has 4 sources and 5 destinations, the linear program for this
will have
A. 4 variables and 5 constraints B 5 variable and 4 constraints
C. 9 variables and 20 constraints D 20 variables and 9 constraints
5. When simulating the Monte Carlo experiment, the average simulated demand over the
long run should approximate the
A. real demand B expected demand
C. sample demand D Daily demand.
6. A company has one computer technician who is responsible for repairs on the
company?s 20 computers. As a computer breaks, the technician is called to make the
repair. If the repairperson is busy, the machine must wait to be repaired. This is an
example of
A. a multichannel system B a finite population system
C. a constant service rate system D a multiphase system

Q.1 (b) Define following: 1) Shadow Prices; 2) Unboundedness; 3) Binary
variables; 4) Global optimum
04

Q.1 (c) Write differences between Assignment Problem Vs Travelling salesman
Problem
04

Q.2 (a) Explain the concept of duality with suitable examples. 07
Page 2 of 4

(b) India Inc., manufactures two products used in the heavy equipment
industry. Both products require manufacturing operations in two
departments. The following are the production time(in hours) and profit
contribution figures for the two products:
Labour Hours
Product Profit per Unit Dept. A Dept. B
1 Rs. 25 6 12
2 Rs. 20 8 10
For the coming production period, India Inc., has available a total of 900
hours of labour that can be allocated to either of the two departments.
Formulate the LPP

07
OR
(b) With a view to improving the quality of customer services, a bank is
interested in making an ?assessment of the waiting time of its customers?
coming to one of its branches located in a residential area. This branch has
only one tellers? counter. The arrival rate of the customers and the service
rate of the teller are given below:
Time Between two consecutive
arrivals of customers
( In minutes)
Probability Service time
by the teller
( In minutes)
Probability
3 0.17 3 0.10
4 0.25 4 0.30
5 0.25 5 0.40
6 0.20 6 0.15
7 0.13 7 0.05
Total 1.00 Total 1.00
You are required to simulate 10 arrivals of customers in the system starting
from 11 AM and show the waiting time of the customers and idle time of
the teller in the analysis table. Use of the following random numbers taking
the pair of random numbers in two digits each for first trial and so on:
(11,56), (23,72), (94,83), (83,02), (97, 99), (83,10), (93,34), (33,53),
(49,94), (37,77); where first random number in the bracket is for arrival and
second random number is for service. Compute probability that the teller is
idle. Hence, determine average inter-arrival time (min) and average
services time (min) using simulation technique. Also determine average.
waiting time of the customers before getting the service and average time
spent by a customer in the bank.
07

Q.3 (a) Explain the concepts of single server queuing model specified by
(M/M/1): (?/FIFO)
07
(b) Geraldine Shawhan is president of Shawhan File Works, a firm that
manufactures two types of metal file cabinets. The demand for her two-
drawer model is up to 600 cabinets per week; demand for a three drawer
cabinet is limited to 400 per week. Shawhan File Works has a weekly
operating capacity of 1,300 hours, with the two-drawer cabinet taking 1
hour to produce and the three-drawer cabinet requiring 2 hours. Each two-
drawer model sold yields a \$10 profit, and the profit for the large model is
\$15. Shawhan has listed the following goals in order of importance:
1. Attain a profit as close to \$11,000 as possible each week.
2. Avoid underutilization of the firm?s production capacity.
3. Sell as many two- and three-drawer cabinets as the demand indicates.
Set this up as a goal programming problem.
07
OR
Q.3 (a) A tailor specializes in ladies? dresses. The number of customers
approaching to the tailor appears to be Poisson distributed with mean of 6
customers per hour. The tailor attends the customers on first come first
serve basis and the customers wait if the need be. The tailor can attend the
07
Page 3 of 4

customers at an average rate of 10 per hour with the service time be
exponentially distributed. Find (i) the utilization factor, (ii) probability that
the system is idle, (iii) the average time that the tailor is free on a 10-hour
working day, (iv) the probability associated with the number of customers;
0 through 3, in the system, (v) expected (average) number of customers in
the shop & expected number of customers waiting for tailor?s service, (vi)
how much time a customer expect to spend in the queue and in the shop?
(vii) Probability that there are more than 3 customers in the shop.
(b) Consider the following LP: Min 2A+2B stc 1A + 3B ? 12; 3A+1B ?13;
1A-1B = 3 and A,B?0. i) Show the feasible region; ii) What are the extreme
points of the feasible region; iii) Find the optimal solution using the
graphical solution procedure
07

Q.4 (a) Compare the similarities and differences of linear and goal programming. 07
(b) A repairman is to be hired by a company to repair machines that
breakdown. Number of breakdown follows Poisson distribution with an
average rate of four per hour. The cost of non-productive machine time is
Rs. 90 per hour. The company has the option of choosing either a fast or a
slow repairman. The fast repairman charges Rs. 70 per hour and will repair
machines at an average rate of 7 machines per hour, while the slow
repairman charges Rs. 50 per hour and will repair at the rate of 6 per hour.
Determine who should be hired.
07
OR
(b) Grey Construction would like to determine the least expensive way of
connecting houses it is building with cable TV. It has identified 11 possible
branches or routes that could be used to connect the houses. The cost in
hundreds of dollars and the branches are summarized in the following table.
What is the least expensive way to run cable to the houses?
Branch Start Node End Node Cost(\$100s)
Branch 1 1 2 5
Branch 2 1 3 6
Branch 3 1 4 6
Branch 4 1 5 5
Branch 5 2 6 7
Branch 6 3 7 5
Branch 7 4 7 7
Branch 8 5 8 4
Branch 9 6 7 1
Branch 10 7 9 6
Branch 11 8 9 2

07

Q.5 XYZ tobacco company purchases and stores in warehouses located in
following four cities:
Warehouse A B C D
Capacity (tones) 90 50 80 60
The warehouses supply tobacco cigarette companies in three cities that have
the following demand:
Cigarette Company Bharat Janta Red Lamp
Demand (tones) 120 100 110
The following railroad shipping costs (in hundred rupees) per ton have been
determined:

14
Page 4 of 4

Warehouse Location Bharat Janta Red Lamp
A ? 10 5
B 12 9 4
C 7 3 11
D 9 5 7
Because of railroad construction, shipments are temporarily prohibited
from warehouse at city A to Bharat Cigarette Company. (a) Find the
optimum distribution for XYZ Tobacco Company and (b) Are there
multiple optimum solutions? If yes, identify them.
OR
Q.5 Suppose Mr. Pavan Kumar is production manager in a manufacturing
company. He has the problem of deciding optimal product mix for the next
month. The company manufactures two products Resistors and Capacitors
which yield unit contribution of Rs. 100 and Rs. 40 respectively. The
company has three facilities (resources) with availability of 1000 kg of raw
material & 900 hrs on machine for the next month. Also 5 workers can work
for 5 hrs a day for 20 days in coming month. It is known that there is
sufficient demand of the products so that all the units produced will be sold
away. Mr. Pavan Kumar collected the relevant data carefully and wants to
solve the problem as Linear Programming model. The relevant data is as
shown in the following table:
Resources Product Resource
Availability Resistors Capacitors
Raw Material 5 2 1000 kg
Machine Capacity 1 2 900 hrs
Workers Availability 1 2 500hrs
Profit (Rs.) ? 100 40

Answer the following questions with justification:

1) Solve the problem using Graphical to determine the optimum product
mix of capacitors and resistors for the next month. Also determiner
corresponding optimum achievable profit due to sells of Resistors and
Capacitors. Which facilities are fully utilized and which resources are left
unused at the optimal stage?

2) Are there alternate (multiple) optimal solutions available to Mr. Pavan
Kumar? If so suggest another solution.

3) Obtain the dual of above problem. Explain the relationship between
optimum solution of given problem and dual LPP. Hence determine the
optimum solution of dual problem.
14

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