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

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

Q.4 (a) What are the advantages and disadvantages of Simulation? 07

(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

Q.4 (a) What are the advantages and disadvantages of Simulation? 07

(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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This post was last modified on 19 February 2020