Quantitative Methods in Business – Linear Programming
1- Statement of the Problem:
Middle East for investment offers a bundle of investment options in many types of securities. Mr. Brown, an investor, would like to invest $ 5 million in various securities. He wishes to maximize his yearly profit over the next year. The investment company offered him a portfolio including Bonds, Stocks, Gold and Land. The expected return is 6% for Bonds, 14% for Stocks, 10% for Gold and 5% for Land. For diversification purposes, the maximum amount to be invested is $ 3 million in Bonds, $ 3 million in Stocks, $ 2 million in Gold and $ 1 million in Land. In addition to that, the investment company specifies that at least 40% of the total investment should be in Bonds and Stocks, and no more than 20% of the total investment should be in land.

2- Formulation:
The decision variables are:
B= Total Dollar amount to be invested in Bonds.
S= Total Dollar amount to be invested in Stocks.
G= Total Dollar Amount to be invested in Gold.
L= Total Dollar Amount to be invested in Land.

The objective function that maximizes the return per year is: Z= 0.06B+0.14S+0.1G+0.05L
Subject to:
1)B+S+G+L≤5,000,000
2)B≤3,000,000
3)S≤3,000,000
4)G≤2,000,000
5)L≤1,000,000
6)B+S≥0.40(B+S+G+L)
→ B+S≥0.4B+0.4S+0.4G+0.4L
→ 0.6B+0.6S-0.4G-0.4L≥0
7)L ≤0.2(B+S+G+L)
→L ≤0.2B+0.2S+0.2G+0.2L
→ -0.2B-0.2S-0.2G+0.8L ≤0
Given that B; S; G and L are positive values
3- POM-QM Output:

4- Analysis:

That is, Mr. Brown needs to invest $ 3 million in stocks and $ 2 million in Gold. The total return would be $ 620,000 and the total return on investment (ROI) would be: Total return/Total amount invested= 620,000/5,000,000= 12.4% The reduced cost for the amount invested in Bonds (B), which is at zero level, is 0.04 (4%). This means that the expected return on Bonds should increase by 4% (from 6% to 10%) in order for B to become non-zero.

...
Exercise 1:
In a management trainee program, 80% of the trainees are female, 10% male. A total of 70% of the females attended college, while 60% of the males attended college. A management trainee is selected at random.
1. What is the probability that the person selected is a female who did NOT attend college?
= 0.80 * 0.30 = 0.24 (24%)
2. What is the probability that the person selected is a female who did attend college?
= 0.80 * 0.70 = 0.56 (56%)
3. What is the probability that the person selected is a male who did NOT attend college?
= 0.10 * 0.40 = 0.04 (4%)
4. What is the probability that the person selected is a male who did NOT attend college?
= 0.10 * 0.40 = 0.04 (4%)
Exercise 2
A group of employees of Unique Services will be surveyed about a new pension plan. In-depth interviews with each employee selected in the sample will be conducted. The employees are classified as follows.
Classification
Event
Number of employees
Supervisors
A
150
Maintenance
B
50
Production
C
1000
Management
D
250
Secretarial
E
60
1. What is the probability that the first person selected is classified as a maintenance employee?
P (B) = 50 ∕ 1510 = 0.033
2. What is the probability that the first person selected is either in maintenance or in secretarial?
P (B U E) = P (B) + P (E) = 0.033+ 0.039 = 0.072
3. What is the probability that the first person selected is either in management or in supervision?
P (D U A) = P (D) + P (A) = 0.165+ 0.099 =...

...Kent Jackson
11AM-12:20PM
GB 202
Quantitative techniques are mathematical and reproducible. Regression analysis is an example of one such technique. Statistical analysis is also an example of a quantitative technique. Quantitative techniques are applied for business analysis to optimize decision making IE profit maximization and cost minimization. It covers linearprogramming models and other special algorithms, inventory and production models.
Albert Humphrey, a management consultant who specialized in organizational management, devised the SWOT analysis technique at Stanford Research Institute in the 1960s. Today, not only large corporations but also nonprofit and government agencies employ SWOT analysis. An enhanced method, known as the Six Forces Model, further helps to quantify competition, buyers and suppliers.
Identify strengths and weaknesses to assess whether the desired end state is possible. If it is not, revise your objective to reflect an attainable goal. Use SWOT analysis in strategic planning, crisis management and feasibility studies. Apply SWOT analysis techniques in academic environments for developmental studies. Use SWOT analysis to figure out how to exploit each strong point and minimize each disadvantage.
SWOT analysis techniques facilitate decision making by classifying and categorizing factors that...

...Quantitative Research MethodsQuantitative means quantity which implies that there is something that can be counted. Quantitative research has been defined in many ways. It is the kind of research that involves the tallying, manipulation or systematic aggregation of quantities of data (Henning, 1986)
John W. Creswell defined quantitative research as an inquiry into a social or human problem based on testing a theory composed a theory composed of variables, measured with numbers, and analysed with statistical procedures in order to determine whether the predictive generalisations of the theory holds true. (Creswell, 2003)
On the other hand, another author defined quantitative research as the collection of numerical data in order to explain, predict and/or control phenomena of interest. Quantitative research is explaining phenomena by collecting numerical data that are analysed using mathematically based methods (Aliaga & Gunderson, 2000)
Quantitative research can also be said to be a research based on traditional scientific methods, which generates numerical data and usually seeks to establish causal relationships (or association) between two or more variables, using statistical methods to test the strength and significance of the relationships (A dictionary of Nursing, 2008)
Simply put, quantitative...

...The development of linearprogramming has been ranked among the most important scientific advances of the mid 20th century. Its impact since the 1950’s has been extraordinary. Today it is a standard tool used by some companies (around 56%) of even moderate size. Linearprogramming uses a mathematical model to describe the problem of concern. Linearprogramming involves the planning of activities to obtain an optimal result, i.e., a result that reaches the specified goal best (according to the mathematical model) among all feasible alternatives.
LinearProgramming as seen by various reports by many companies has saved them thousands to even millions of dollars. Since this is true why isn’t everyone using LinearProgramming? Maybe the reason is because there has never been an in-depth experiment focusing on certain companies that do or do not use linearprogramming. My main argument is that linearprogramming is one of the most optimal ways of resource allocation and making the most money for any company today.
I used (in conjunction with another field supporter – My Dad) the survey method to ask 28 companies that were in Delaware, New Jersey, and Pennsylvania whether they were linearprogramming users. In addition, I wanted to examine...

...
2. Total Profit Contribution Regular Mix Deluxe Mix Holding Mix
Total
$33,750
Almond
Brazil
Filbert
Pecan
Walnut
Available Regular Mix Deluxe Mix Holding Mix nut available after saling
6000
1500 600 1250 2650
7500
2500 600 7 50 3650
7500
2500 600 750 3650
6000
1000 600 1250 3150
7500
2500 600 1000 3400
*
So, purchasing more nuts will not increase profit because we already have enough of nuts. 4. TJ's does not have to purchase an additional 1000 pounds of almonds, because there are 2650 pounds are not used yet.
5. If that happen, then the profit contribution could be increased by concentrate on producing Holding Mix, because it has high profit than other.
Dr. Taqi N. Al-Faraj QuantitativeMethods for Management OM 310 Case Studies
Case Problem
Page in Textbook
Group
Workload Balancing Production Strategy Hart Venture Capital Product Mix Investment Strategy Truck Leasing Strategy Planning an Advertising Campaign Phoenix Computer Textile Mill Scheduling Workforce Scheduling Cinergy Coal Allocation Distribution System Design Textbook Publishing Yeager National Bank Production Scheduling with Changeover Costs Ambulance Routing R.C. Coleman
...

...Phoenix Computer
1. The incremental salary and training cost associated with hiring a new employee and training him/her to be laptop specialist.
* Annual salary for new employee = $27,000
* Cost for three month training program = $1,500 per person
* New employee undergoes three month training
$27,000/12 = $2,250
$2,250*3 months = $6,750
$6,750 + $1,500 =$8,250 per person
The incremental salary and training cost associated with hiring a new employee and training him/her to be laptop specialist is $8,250 per person.
2. The incremental salary and training cost associated with putting a current employee through the training program.
* Annual salary for new employee = $27,000
* Cost for two months training program = $1,000
* Current employee undergoes two months training.
$27,000/12 = $2,250 per month
$2,250*2 months = $4,500
$4,500 + $1,000 = $5,500 per person
The incremental salary and training cot associated with putting a current employee through the training program is $5,500 per person.
3. Recommendations regarding the hiring and training plan that will minimize the salary and training cost over February through August period.
New employee = N
Current Employee = C
Extra employee = E
Variables: Training Period
New employee undergoes three months training
N1 = February to April
N2 = March to May
N3 = April to June
N4 = May to July
N5 = Jun to August
Current employee undergoes two...

...ETHICS IN
BUSINESS RESEARCH
Mian Umair Asghar
Week 4
Global Institute DHA
INTRODUCTION
Ethics are norms or
standards of behavior that
guide moral choices about
our behavior and our
relationships with others.
The goal is to ensure that
no one is harmed or suffers
adverse consequences from
INTRODUCTION
Begin data collection by explaining to
the respondent the benefits expected
from the research.
Explain to the respondents that their
rights and well-being will be
adequately protected, and say how this
will be done.
Be certain that interviewers obtain the
informed consent of the respondent.
Research Ethics
1. Non-Discrimination
Avoid discrimination against colleagues or students on
the basis of sex, race, ethnicity, or other factors that
are not related to their scientific competence and
integrity.
2. Objectivity
Strive to avoid bias in experimental design, data
analysis, data interpretation, peer review, personnel
decisions, grant writing, expert testimony, and other
aspects of research where objectivity is expected or
required. Avoid or minimize bias or self-deception.
Disclose personal or financial interests that may affect
research.
Research Ethics
3. Carefulness
Avoid careless errors and negligence; carefully
and critically examine your own work and the
work of your peers. Keep good records of
research activities, such as data collection,
research design, and correspondence with
agencies or journals.
4. Legality
Know and obey relevant...

...TOPIC – LINEARPROGRAMMINGLinearProgramming is a mathematical procedure for determining optimal allocation of scarce resources.
Requirements of LinearProgramming
• all problems seek to maximize or minimize some quantity
• The presence of restrictions or constraints
• There must be alternative courses of action
• The objective and constraints inlinearprogramming must be expressed in terms of linear equations or
inequalities
Objective Function it maps and translates the input domain (the feasible region) into output range, with
the two-end values called the maximum and minimum values
Restriction Constraints it limits the degree to which we can pursue our objective
Decision Variables represents choices available to the decision maker in terms of amount of either inputs or outputs
Parameters these are the fixed values in which the model is solved
Basic Assumption of LinearProgramming
1. Certainty- figures or number in the objective and constraints are known with certainty and do not vary
1. Proportionality - for example 1:2 is equivalent to 5:10
1. Additivity - the total of all the activities equals the sum of the individual...

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