Assignment Code: 2011GM03A1Last Date of Submission: 31st March 2011
Maximum Marks:100

Attempt all the questions. All the questions are compulsory and carry equal marks.

Section-A

Ques.1In a certain examination there were 100 candidates of whom 21 failed, 6 secured distinctions, 43 were placed in third division and 18 in the second division. It is known that at least 75% marks are required for distinction, at least 40% for passing, at least 50% for second division and at least 60% for first division.

Calculate the median of the distribution of marks

Ques.2The pass result of 50 students who took a class test is given below:

If the mean mark for all the students was 51.6, find the mean marks of students who failed

Ques.3Define skewness. When does a distribution get positively and negatively skewed?

Ques.4A Wholesale distributor of a product finds that the annual demand for a product is normally distributed with the mean of 120 and the standard deviation of 16. If he orders only once a year, what quantity should be ordered to ensure that there is only a 5 percent chance of running short (Area between (= 0 and (=1.64 is 0.45, where ( in the standard normal variate).

Section-B

Case Study

A business graduate very much wants to get a job in any one of the top 10 accounting firms. Applying to any one of these companies requires a lot of effort and paperwork and is therefore costly. She estimates the cost of applying to each of 10 companies and the probability of getting a job offer there. These data are tabulated below. The tabulation is in the decreasing order of cost.

...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 to obtain the initial feasible solution to a transportation problem.
Discuss the various methods of finding initial feasible solution of a transportation problem and state the advantages, disadvantages, and areas of application for them.
5. What is an assignment problem? It is true to say that it is a special case of the transportation problem? Explain. How can you formulate an assignment problem as a standard linear...

...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 identifiable
and measurable, making their inclusion in the
model relatively easy.
In contrast, qualitative factors measure such
things as perceptions, feelings, and opinions.
Although some qualitative factors do have scales
of measures (for example, we can classify
opinions of the President’s performance as good,
fair, or poor), in general, they are difficult to
quantify and measure
Spreadsheet packages are capable of handling many decision
modeling techniques
Some advantages of using spreadsheets for decision modeling
are:
spreadsheets are capable of quickly calculating results for a
given set of input values
spreadsheets are effective tools...

...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...

...This article appeared in Corporate page of The Edge Malaysia, Issue 814, July 12 - 18, 2010
Quantitative Analysis… for football managers
By Jasvin Josen
In the heat of the world cup it is worthy to reflect on how football has impacted the financial world and what it could mean for the future. The amount of money generated by the football industry grew exponentially in the late 1990s and early 2000s, and has been steadily growing since. Record-breaking financial deals have been negotiated between football clubs and players they sign. With the fast moving pace of the industry, clubs and players are bound to undergo some sort of financial advancement into the future. Shares in clubs are a reality now. Eventually, players will want to establish themselves as corporations and to issue shares in themselves. Sooner or later, it would make financial sense to hedge clubs or players’ performance with derivatives. Thus there is a real need to quantitatively evaluate a football player, to understand his value adding potential, and to put a price upon that capacity.
Existing conditions already show a growing need to measure the value of a football player. Chelsea spent £24m for Didier Drogba in 2004. Real Madrid spent £80 million on Cristiano Ronaldo in June 2009. We can only guess what the price may be for Lionel Messi if he leaves Barcelona. Yet at times, this spending is claimed to have contributed to financial problems, especially when the...

...Introduction
A person managing a production unit, where it is a farm, factory, or domestic kitchen, has to coordinate men, machines, and money against several constraints like that of time, cost and space, in order to achieve the organizations objectives in an efficient and effective manner.
The manager has to analyze the situation on a continuous basis, determine the objectives, identify the best options from the set of available alternatives, implement, coordinate, evaluate and control the situation continuously to achieve these objectives
Definitions
Quantitativetechniques are those statistical and programming techniques, which help decision makers solve many problems, especially those concerning business and industry
Quantitativetechniques are those techniques that provide the decision makers with systematic and powerful means of analysis, based on quantitative data, for achieving predetermined goals
These techniques involve the use of numbers symbols, mathematical expressions, other elements of quantities, and serve as supplements to the judgment and intuitions of the decision makers
Evolution
The utility of quantitativetechniques has been realized long ago and the science of mathematics is probably as old as the human society
The evolution of industrial engineering, scientific...

...
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 calculated by...

...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...

...Centre for Continuing Education
Executive MBA
(OIL & GAS Management)
Batch: _______________________
Semester: _______________________
Name: _______________________
Sap No/Regn No: _______________________
Assignment – 1
For
QuantitativeTechniques 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...