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.

...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...

...and 30 are regular. The rate of production for each fabric on each
type of loom is given in Table 2. The time required to change over from producing one fabric to
another is negligible and does not have to be considered.
Loom Rate (yards/hour)
Fabric
Dobbie
Regular
1
4.63
--2
4.63
--3
5.23
5.23
4
5.23
5.23
5
4.17
4.17
TABLE 2 – LOOM PRODUCTION RATES FOR THE SOUTHERN TEXTILE MILL
The Southern Textile Mill satisfies all demand with either its own fabric or fabric purchased
from another mill. Fabrics that cannot be woven at the Southern Mill because of limited loom
capacity will be purchased from another mill. The purchase price of each fabric is also shown in
Table 1.
MANAGERIAL REPORT
I. -
Develop a LinearProgramming Model that can be used to schedule production for the
Southern Textile Mill, and at the same time to determine how many yards of each fabric
must be purchased from another mill. The model should be clear and complete.
II. -
Include the corresponding spreadsheet of the model developed in part I and obtain the
optimal solution using “SOLVER.” (Annotate your spreadsheet as needed).
III. -
A discussion and analysis of the following items in your report.
1.
2.
3.
The final production schedule and loom assignments for each fabric
The projected total contribution to profit
A discussion of the value of additional loom time. (The mill is considering
purchasing a ninth dobbie loom....

...to eschew status signifiers and develop close, caring relationships with their co-workers. Interactions between co-workers and managers are characterized by informality and egalitarianism. Managers are encouraged to not take themselves too seriously, to show “equalness,” involve co-workers in decisions and exhibit characteristics of “humbleness” when interacting with others.
Q2 Critically analyse how aspects of the “IKEA-way” have caused problems in its overseas experiences in Germany, France and the United States
While IKEA’s culture has been a strong factor in its competitive advantage, its expansion into overseas locations has also brought challenges, when in-country cultural norms clashed with IKEA’s preferred way of doing business. In Germany, IKEA’s liking for informal relations between co-workers and managers has been interpreted as undermining the respect and prestige traditionally given to a boss. Also, the German worker is felt to be more comfortable with detailed procedures and work instructions, which contradicts with IKEA’s belief in minimizing bureaucracy and burdensome administration. In France, IKEA’s informality has been interpreted as a sign of weakness, or indecision. Also, its preference for not recognizing status is felt to cause an identity problem as everyone is on the same level. However, it is perhaps in the US that cultural differences have been most profound. Swedes traditionally value muted and controlled emotions,...

...ON
LINEARPROGRAMMING
Vikas Vasam
ID: 100-11-5919
Faculty: Prof. Dr Goran Trajkovski
CMP 561: Algorithm Analysis
VIRGINIA INTERNATIONAL UNIVERSITY
Introduction:
One of the section of mathematical programming is linearprogramming.
Methods and linearprogramming models are widely used in the optimization of processes in all sectors of the economy: the development of the production program of the company, its distribution on the performers, when placing orders between the performers and the time intervals, to determine the best range of products, in problems of perspective, current and operational planning and management, traffic planning, defining a plan of trade and distribution, in the problems of development and distribution of productive forces, bases and depots of material handling systems, resources, etc. especially widely used methods and linearprogramming model for solving problems are savings (choice of resource-saving technologies, preparation of mixes, nesting materials), production, transportation and other tasks.
Beginning of linearprogramming was initiated in 1939 by the Soviet mathematician and economist Kantorovich in his paper "Mathematical methods of organizing and planning...

...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...

...
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
...

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