Centre for Continuing Education
Executive MBA
(OIL & GAS Management)
Batch: _______________________
Semester: _______________________
Name: _______________________
Sap No/Regn No: _______________________
Assignment – 1
For
Quantitative Techniques for Management Applications
MBCQ -721
University of Petroleum & Energy Studies
Last Date to submit Assignment-1:-15th Sep 2012
SECTION A (TOTAL MARKS 20)
Each question carries equal marks. Attempt all.

1. Point out the assumptions of Linear Programming. Solve the following by using graphical method; Maximize z =- 5y, subject to x +y ≤ 1, 0.5x + 5y ≥ 0, and x ≥ 0, y ≥ 0. 2. Explain the meaning of two person zero sum game. Define saddle point in a game. Clearly explain the rules of dominance for a game. 3. Define Binomial & Poisson Distributions. A problem in QT is given to three students A, B, and C whose chances of solving it are ½, ¾ and ¼ respectively. What is the probability that the problem will be solved if all of them try independently? 4. Explain the difference and relation between a transportation & assignment problem. SECTION B (TOTAL MARKS 30)

Each question carries Equal marks. Attempt all.
5. a) In a petroleum engineering workshop there are seven machines for drilling, two for turning, three for milling and one for grinding. Four types of brackets are made. Type A is found by work study to require 7 minutes drilling, 3 minutes turning, 2.5 minutes milling, and 1.5 minutes grinding, and the corresponding times in minutes for the other types are: B: 5, 0, 1.5,0.5 ; C: 14, 6, 9, 3.5 ; D: 26, 9, 11, 1.5. How many of each type of brackets should be produced per hour in order to keep all the machines fully occupied? b) A manufacturer of printed fabrics has three machines, that prepare raw fabric and five machines that print on it. Two types of printed fabrics are produced; type A requires 3 minutes per meter to prepare and 6 minutes per meter to print, while type B...

...LIBA
Quantitative Assignment - 1
P 12 - Batch: Students Profile
Submitted To:
Prof. P Lakshmanan
Submitted By:
Group
Contents
|S.No. |Title |Page No. |
|1. |Synopsis |3 |
|2. |Objective |3 |
|3. |Process Chart |4 |
|4. |Limitations |4 |
|5. |Quantitative Tools |4 |
|6. |Analysis |5 |
|7. |Conclusion |15 |
1. Synopsis:
This assignment is taken up in order to understand the personnel profile and behavioral pattern of students who undertake the part time PGDM courses in LIBA. Inferences are drawn from...

...NTITATIVE MGNT
QUANTITATIVEAPPLICATIONS IN MANAGEMENT
Course Code: MIB 105 Credit Units: 03
Course Objective:
The objective of this course is to develop the understanding of the various statistical models, used for decisions making in the functions of the management of any organization with respect to International Business. To equip the students with tools and techniques for application of concepts to real life problems for efficient managerial decision making.
Learning Outcomes:
At the end of the course students will be able to:
Use statistical techniques to collect and analyse data
Produce forecasts using statistical packages
Apply quantitativetechniques to business situations.
Course Contents:
Module I: Introduction
Quantitative Decision Making - an overview,
Collection , Classification & Presentation of Data,
Measures of Central Tendency - Mean, Median, Mode, Geometric Mean & Harmonic Mean,
Measures of Dispersion – Range, Quartile Deviation, Average Deviation & Standard Deviation.
Module 2 : Probability , Probability Distributions & Decision theory
Basic Concepts of Probability
Discrete Probability Distribution
Continuous Probability Distributions
Decision Theory : introduction to decision making & decision environments
Module 3 Sampling , Sampling Distributions & Testing of...

...Sub: QuantitativeTechniques in Management
1) Answer any Sixteen
1. What is a linear programming problem? Discuss the scope and role of
linear programming in solving management problems. Discuss and
describe the role of linear programming in managerial decision-making
bringing out limitations, if any.
2. Explain the concept and computational steps of the simplex method for
solving linear programming problems. How would you identify whether an
optimal solution to a problem obtained using simplex algorithm is unique
or not?
a) What is the difference between a feasible solution, a basic feasible
solution, and an optimal solution of a linear programming problem?
b) What is the difference between simplex solution procedure for a
`maximization’ and a `minimization’ problem?
c) Using the concept of net contribution, provide an intuitive
explanation of why the criterion for optimality for maximization
problem is different from that of minimization problems.
Outline the steps involved in the simplex algorithm for solving a linear
programming maximization problem. Also define the technical terms used
therein.
3. ``Linear programming is one of the most frequently and successfully
employed Operations Research techniques to managerial and business
decisions.’’ Elucidate this statement with some examples.
…2…
…2…
4. Describe the transporation problem and give its mathematical model.
Explain,...

...QTM Quiz 4
Set A
1. Out of a population of 60 people, the standard error comes to 1.65kg when calculating their average weight using sampling with replacement and 1.61 when using sampling without replacement. What is the sample size and standard deviation of the population? (4)
N=60
With replacement, S.E. =
Without replacement, S.E. = = 1.61
Thus, FPC = (N-n)/(N-1) =
Thus, 60-n = 56.174
Thus, n = 3.8 or 4 approx.
2. When calculating the average income of the residents in a housing complex, how many samples must be taken to ensure the sample mean is within Rs. 10,000 of the original 99% of the time, the standard deviation being Rs.1,00,000? (4)
Thus, and
Thus,
Now, P(|Z|)≥0.99 means P(Z) = 0.995, -2.58 ≤ Z ≤ 2.58,
Thus, 2.58 ≤ 0.1, so n ≥ 665.64 ≈ 666
3. If you are out to measure the most common brand of privately owned automobile in a country, describe how you would set up the experiment, including objective, response variable and sampling type. Justify your answer. (2)
Note: Your answer can be different as long as it is logically presented
Population: All private automobile owners in the country
Objective: To determine the distribution of automobile brands and identify the most common.
Response variable: Brand of automobile privately owned by a person
Sampling process: Use prior judgment and calculations to (a) determine sample size and (b) identify clusters that are representative of the population. Use simple...

...What is a linear programming problem? Discuss the scope and role of linear programming in solving management problems. Discuss and describe the role of linear programming in managerial decision-making bringing out limitations, if any.
2. Explain the concept and computational steps of the simplex method for solving linear programming problems. How would you identify whether an optimal solution to a problem obtained using simplex algorithm is unique or not?
a) What is the difference between a feasible solution, a basic feasible solution, and an optimal solution of a linear programming problem?
b) What is the difference between simplex solution procedure for a `maximization’ and a `minimization’ problem?
c) Using the concept of net contribution, provide an intuitive explanation of why the criterion for optimality for maximization problem is different from that of minimization problems.
Outline the steps involved in the simplex algorithm for solving a linear programming maximization problem. Also define the technical terms used therein.
3. ``Linear programming is one of the most frequently and successfully employed Operations Research techniques to managerial and business decisions.’’ Elucidate this statement with some examples.
…2…
…2…
4. Describe the transporation problem and give its mathematical model. Explain, by taking an illustration, the North-West Corner Rule, the Least Cost Method and the Vogel’s Approximation Method...

...professional organizations support the
use of the scientific approach:
the Institute for Operation Research and Management Science
(INFORMS)
the Decision Sciences Institute (DSI)
the Production and Operations Management Society (POMS)
the Academy of Management.
Organizations such as American Airline, United Airlines, IBM,
Google, UPS, FedEx etc
Deterministic means with complete certainty
Deterministic models assume that all the relevant input
data are known with certainty. That is, these models
assume that all the information needed for modeling the
decision-making problem environment is available, with
fixed and known values
For example, deciding how many sections of a course to
offer during a semester can be modeled as a deterministic
model since the costs and benefits of offering each section
are known. The most commonly used deterministic
modeling technique is Linear Programming
Probabilistic (also called stochastic) models
assume that some input data are not known with
certainty
That is, these models assume that the values of
some important variables will not be known before
decisions are made
For Example this type of model is the decision of
whether to start a new business venture. As we seen
with high variability in the stock market during the
past several years the success of such venture is
unsure.
Quantitative factors are typically...

...
QuantitativeTechniques in Management
Assignment A
1. From the following data calculate the missing the missing frequency.
No. of
tablets
4-8 8-12 12-16 16-20 20-24 24-28 28-32 32-36 36-40
No. of
Persons
Cured
11 13 16 14? 9 17 6 4
The average number of tablets to curve fever was 19.9.
Solution:
No. of tablets
Mid point
No. of persons cured
Product
4-8
6
11
66
8-12
10
13
130
12-16
14
16
224
16-20
18
14
252
20-24
22
x
22x
24-28
28-32
26
30
9
17
234
510
32-36
34
6
204
36-40
38
4
152
1772+22x/90+x=19.9
1772+22x=1791+19.9x
2.1x=19
X= 9
Hence the missing frequency 20-24= 9
2. You are supplied the following data about heights of students in a college.
Boys Girls
Number 72 38
Average height (inches) 68 61
Variance of distribution 9 4
Find out:
(a). In which sex, boys or girls, is there greater variability in individual heights.
(b). Common average heights in boys and girls.
(c). Standard deviation of height of boys and girls taken together.
(d). Combined variability.
a. C.V of boys height = σ¹/x×100=√9/68=4.41%
(a) C.V of girls height = σ²/x ×100=√4/61×100=3.28%
Thus there is greater variability in the height of boys than girls,
(b) height of boys and girls combined is
̅x¹²=N¹̅x¹+N²̅x²/N¹+N²=
72×68+38×61/72+38=7214/110=65.58 inches approx.
(c) the combined standard deviation may be...

...QuantitativeTechniques/Operations Research
Successful managers use quantitativetechniques in decision making when:
1. The problem is complex.
2. The problem involves many variables.
3. There are data which describe the decision environment.
4. There are data which describe the value or utility of the different possible alternatives.
5. The goals of the decision maker or the organization can be described in quantitative terms.
6. Workable models are available for these situations.
Six steps towards making better decisions:
Process Activities Process Steps Process Output
1. Site visits Observe the problem Sufficient information
Conferences environment and support to proceed
Observation
Research
2. Define use Analyze and define Clear grasp of need for
Define objectives and nature of solution
Define limitations requested
3. MS/OR tools Develop a model Model that works under
Interrelationships identified limitations
Mathematical models
Known solutions
Research
4. Internal/external data Select appropriate data Sufficient inputs to
Facts input operate and test model
Opinions
Computer data banks
5. Testing Provide a solution and Solution(s) that support
Limitations test its reasonableness current organizational
Verification...