Download JNTUH (Jawaharlal Nehru Technological University Hyderabad) MBA (Master of Business Administration) 2nd Semester (Second Semester) R17 2019 Dec 742AD Quantitative Analysis For Business Decisions Previous Question Paper
Code No: 742AD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
MBA II Semester Examinations, December - 2019
QUANTITATIVE ANALYSIS FOR BUSINESS DECISIONS
Time: 3hours Max.Marks:75
Note: This question paper contains two parts A and B.
Part A is compulsory which carries 25 marks. Answer all questions in Part A. Part B
consists of 5 Units. Answer any one full question from each unit. Each question carries
10 marks and may have a, b, c as sub questions.
PART - A 5 ? 5 Marks = 25
1.a) What is a model? What purpose does it serve? [5]
b) What is duality in Linear Programming problem? [5]
c) What is an unbalanced assignment problem? Illustrate your answer with example. [5]
d) i) What is cost slope?
ii) Distinguish between PERT&CPM. [5]
e) For the GI/G/1, FCFS model, using the basic definitions and relationships, verify the
following relationships:
i) L = L
q
+ (1 - P
0
) ii) L = L
q
+ ? iii) P
0
= 1 - ? [5]
PART - B 5 ? 10 Marks = 50
2.a) Explain briefly the steps (perhaps overlapping) involved in an Operations Research
Study.
b) A company having a mechanical workshop has recently discontinued production of an
unprofitable product. It has resulted in a considerable spare capacity. The company has
decided to use this capacity to the maximum extent to produce three products which
are profitable. The productivity coefficient in machine hours per unit and available
machine time is given below:
Machine type Product 1 Product 2 Product 3 Time Available
Machine Hours per week
Milling Machine
Lathe
Grinder
9
5
3
3
4
0
5
0
2
500
350
150
The sales department has indicated that the demand for Products 1 and 2 exceeds the
maximum production rate whereas sales potential for Product 3 is 20 units per week.
The profits for the three products have been estimated respectively as Rs. 3500,
Rs.1400, and Rs. 1750 for the three products. The company wants to decide the
optimum level of production to maximize its profit.
Formulate this problem as a mathematical model. [5+5]
OR
3.a) Write a short note on Sensitivity analysis and its importance.
b) Consider the following problem:
Minimize ?? = 5 ?? 1
+ 7 ?? 2
,
Subject to,
2 ?? 1
+ 3 ?? 2
? 42,
3 ?? 1
+ 4 ?? 2
? 60,
?? 1
+ ?? 2
? 18,
and ?? 1
? 0, ?? 2
? 0.
Solve this problem graphically and explain briefly the steps involved in reaching the
optimum solution. [4+6]
R17
S
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Code No: 742AD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
MBA II Semester Examinations, December - 2019
QUANTITATIVE ANALYSIS FOR BUSINESS DECISIONS
Time: 3hours Max.Marks:75
Note: This question paper contains two parts A and B.
Part A is compulsory which carries 25 marks. Answer all questions in Part A. Part B
consists of 5 Units. Answer any one full question from each unit. Each question carries
10 marks and may have a, b, c as sub questions.
PART - A 5 ? 5 Marks = 25
1.a) What is a model? What purpose does it serve? [5]
b) What is duality in Linear Programming problem? [5]
c) What is an unbalanced assignment problem? Illustrate your answer with example. [5]
d) i) What is cost slope?
ii) Distinguish between PERT&CPM. [5]
e) For the GI/G/1, FCFS model, using the basic definitions and relationships, verify the
following relationships:
i) L = L
q
+ (1 - P
0
) ii) L = L
q
+ ? iii) P
0
= 1 - ? [5]
PART - B 5 ? 10 Marks = 50
2.a) Explain briefly the steps (perhaps overlapping) involved in an Operations Research
Study.
b) A company having a mechanical workshop has recently discontinued production of an
unprofitable product. It has resulted in a considerable spare capacity. The company has
decided to use this capacity to the maximum extent to produce three products which
are profitable. The productivity coefficient in machine hours per unit and available
machine time is given below:
Machine type Product 1 Product 2 Product 3 Time Available
Machine Hours per week
Milling Machine
Lathe
Grinder
9
5
3
3
4
0
5
0
2
500
350
150
The sales department has indicated that the demand for Products 1 and 2 exceeds the
maximum production rate whereas sales potential for Product 3 is 20 units per week.
The profits for the three products have been estimated respectively as Rs. 3500,
Rs.1400, and Rs. 1750 for the three products. The company wants to decide the
optimum level of production to maximize its profit.
Formulate this problem as a mathematical model. [5+5]
OR
3.a) Write a short note on Sensitivity analysis and its importance.
b) Consider the following problem:
Minimize ?? = 5 ?? 1
+ 7 ?? 2
,
Subject to,
2 ?? 1
+ 3 ?? 2
? 42,
3 ?? 1
+ 4 ?? 2
? 60,
?? 1
+ ?? 2
? 18,
and ?? 1
? 0, ?? 2
? 0.
Solve this problem graphically and explain briefly the steps involved in reaching the
optimum solution. [4+6]
R17
S
4. David, LaDeana and Lydia are the sole partners and workers in a company which
produces fine clocks. David and LaDeana each are available for 40 hours per week at
the company, while Lydia is available to work for a maximum of 20 hours per week.
The company makes two different types of clocks: a grand-father clock and a wall
clock. To make a clock, David (a mechanical engineer) assembles the inside
mechanical parts of the clock while LaDeana (Woodworker) produces the hand carved
wood casings. Lydia is responsible for taking orders and shipping the clocks. The
amount of time required for each of these tasks is shown below:
Time Required
Grandfather Clock Wall Clock
Assemble clock mechanism
Carve wood casing
Shipping
6 hours
8 hours
3 hours
4 hours
4 hours
3 hours
Each grandfather clock built and shipped yields a profit of $300, while each wall clock
yields a profit of $200.
Three partners now want to determine how many clocks of each type should be
produced per week to maximize the total profit.
a) Formulate a linear programming model in algebraic form for the problem.
b) Solve this problem. [10]
OR
5. There are 3 sources and four destinations with the costs of transportation are as shown
in the following table.
Source
Destination
Supply 1 2 3 4 5
1
2
3
8
5
6
6
?
3
3
8
9
7
4
6
5
7
8
20
30
30
25 25 20 10 20
Balance this transportation matrix and solve for optimal solution. [10]
6. For the following problem begin with Hungarian Method and using iterations solve for
optimal solution. [10]
Assignee
Task
1 2 3 4
A
B
C
D
4
7
4
5
6
4
7
3
5
5
6
4
5
6
4
7
OR
7. Consider the assignment problem with following cost matrix:
Person
Job
1 2 3
A
B
C
5
3
2
7
6
3
4
5
4
Formulate this problem as a linear programming problem and solve. [10]
S
FirstRanker.com - FirstRanker's Choice
Code No: 742AD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
MBA II Semester Examinations, December - 2019
QUANTITATIVE ANALYSIS FOR BUSINESS DECISIONS
Time: 3hours Max.Marks:75
Note: This question paper contains two parts A and B.
Part A is compulsory which carries 25 marks. Answer all questions in Part A. Part B
consists of 5 Units. Answer any one full question from each unit. Each question carries
10 marks and may have a, b, c as sub questions.
PART - A 5 ? 5 Marks = 25
1.a) What is a model? What purpose does it serve? [5]
b) What is duality in Linear Programming problem? [5]
c) What is an unbalanced assignment problem? Illustrate your answer with example. [5]
d) i) What is cost slope?
ii) Distinguish between PERT&CPM. [5]
e) For the GI/G/1, FCFS model, using the basic definitions and relationships, verify the
following relationships:
i) L = L
q
+ (1 - P
0
) ii) L = L
q
+ ? iii) P
0
= 1 - ? [5]
PART - B 5 ? 10 Marks = 50
2.a) Explain briefly the steps (perhaps overlapping) involved in an Operations Research
Study.
b) A company having a mechanical workshop has recently discontinued production of an
unprofitable product. It has resulted in a considerable spare capacity. The company has
decided to use this capacity to the maximum extent to produce three products which
are profitable. The productivity coefficient in machine hours per unit and available
machine time is given below:
Machine type Product 1 Product 2 Product 3 Time Available
Machine Hours per week
Milling Machine
Lathe
Grinder
9
5
3
3
4
0
5
0
2
500
350
150
The sales department has indicated that the demand for Products 1 and 2 exceeds the
maximum production rate whereas sales potential for Product 3 is 20 units per week.
The profits for the three products have been estimated respectively as Rs. 3500,
Rs.1400, and Rs. 1750 for the three products. The company wants to decide the
optimum level of production to maximize its profit.
Formulate this problem as a mathematical model. [5+5]
OR
3.a) Write a short note on Sensitivity analysis and its importance.
b) Consider the following problem:
Minimize ?? = 5 ?? 1
+ 7 ?? 2
,
Subject to,
2 ?? 1
+ 3 ?? 2
? 42,
3 ?? 1
+ 4 ?? 2
? 60,
?? 1
+ ?? 2
? 18,
and ?? 1
? 0, ?? 2
? 0.
Solve this problem graphically and explain briefly the steps involved in reaching the
optimum solution. [4+6]
R17
S
4. David, LaDeana and Lydia are the sole partners and workers in a company which
produces fine clocks. David and LaDeana each are available for 40 hours per week at
the company, while Lydia is available to work for a maximum of 20 hours per week.
The company makes two different types of clocks: a grand-father clock and a wall
clock. To make a clock, David (a mechanical engineer) assembles the inside
mechanical parts of the clock while LaDeana (Woodworker) produces the hand carved
wood casings. Lydia is responsible for taking orders and shipping the clocks. The
amount of time required for each of these tasks is shown below:
Time Required
Grandfather Clock Wall Clock
Assemble clock mechanism
Carve wood casing
Shipping
6 hours
8 hours
3 hours
4 hours
4 hours
3 hours
Each grandfather clock built and shipped yields a profit of $300, while each wall clock
yields a profit of $200.
Three partners now want to determine how many clocks of each type should be
produced per week to maximize the total profit.
a) Formulate a linear programming model in algebraic form for the problem.
b) Solve this problem. [10]
OR
5. There are 3 sources and four destinations with the costs of transportation are as shown
in the following table.
Source
Destination
Supply 1 2 3 4 5
1
2
3
8
5
6
6
?
3
3
8
9
7
4
6
5
7
8
20
30
30
25 25 20 10 20
Balance this transportation matrix and solve for optimal solution. [10]
6. For the following problem begin with Hungarian Method and using iterations solve for
optimal solution. [10]
Assignee
Task
1 2 3 4
A
B
C
D
4
7
4
5
6
4
7
3
5
5
6
4
5
6
4
7
OR
7. Consider the assignment problem with following cost matrix:
Person
Job
1 2 3
A
B
C
5
3
2
7
6
3
4
5
4
Formulate this problem as a linear programming problem and solve. [10]
S
8. An investment of $10,000 in a high risk venture has a 50-50 chance over next year of
increasing to $14,000 or decreasing to 8,000. Thus the net return can be either $4,000
or -$2,000.
a) Assuming a risk-neutral investor and a utility scale from 0 to 100, determine the
utility of $0 net return on investment and associated indifference probability.
b) Suppose the two investors A and B have exhibited the following indifference
probabilities:
Net Returns ($)
Indifference Probability
Investor A Investor B
-2000
-1000
0
1000
2000
3000
4000
1.00
0.30
0.20
0.15
0.10
0.05
0.00
1.00
0.90
0.80
0.70
0.50
0.40
0.00
Graph the utility functions for investors A and B, and categorize each investor as either
a risk averse person or a risk seeker. [10]
OR
9. A company is in the process of preparing a budget for launching a new product. The
following table provides the associated activities and their durations. Construct the
project network. [10]
Activity Predecessors Duration (days)
A:
B:
C:
D:
E:
F:
G:
Forecast Sales volume
Study competitive market
Design item and facilities
Prepare production schedule
Estimate cost of production
Set sales price
Prepare Budget
-
-
A
C
D
B, E
E, F
10
7
5
3
2
1
14
10. On an average 96 patients per 24-hours day require the service of an emergency clinic.
Also on an average, a patient requires 10 minutes of active attention. Assume that the
facility can handle only one emergency at a time. Suppose that it costs the clinic Rs. 100
per patient treated to obtain an average servicing time of 10 minutes, and that each
minute of decrease in this average time would cost Rs. 10 per patient treated. How much
would have to be budgeted by the clinic to decrease the average size of the queue from
1
1
3
patients to
1
2
patient. [10]
OR
11.a) Explain two-person zero-sum game by giving suitable example
b) Explain Minimax and Maxmin principles in solving games.
c) What is the saddle point?
d) Define the value of a game.
e) Solve the following game by giving optimum strategies for each player and value of
the game: [10]
Player B
B1 B2 B3 B4
Player A
A1 3 3 1 10
A2 5 5 4 6
A3 4 -2 0 -5
--ooOoo--
S
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This post was last modified on 23 October 2020