Raptor Fuels produces three grades of gasoline Regular, Premium, and Super. All of these are produced by blending two types of crude oil Crude A and Crude B. The two types of crude contain specific ingredients which help in determining the octane rating of gasoline. The important ingredients and the costs are contained in the following table: [pic]

.:.
In order to achieve the desired octane ratings, at least 41% of Regular gasoline should be Ingredient 1; at least 44% of Premium gasoline must be Ingredient 1, and at least 48% of Super gasoline must be Ingredient 1. Due to current contract commitments, Raptor Fuels must produce as least 20,000 gallons of Regular, at least 15,000 gallons of Premium, and at least 10,000 gallons of Super. Formulate a linear program that could be used to determine how much of Crude A and Crude B should be used in each of the gasolines to meet the demands at the minimum cost. What is the minimum cost? How much of Crude A and Crude B are used in each gallon of the different types of gasoline?

A1 = 18,333.33 gallons of crude A used in Regular; A2 = 10,000 gallons of crude A used in Premium; A3 = 3,333.33 gallons of crude A used in Super; B1 = 1.666.67 gallons of crude B used in Regular, B2 = 5,000 gallons of crude B used in Premium; B3 = 6,666.67 gallons of crude B used in Super; total cost =...

...Quantitative Techniques/Operations Research
Successful managers use quantitative techniques 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 inquantitative 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 objectives
6. Behavioral issues...

...Final Assignment Take-Home Exam – Example Solutions
QUANTITATIVEANALYSIS AND BUSINESS DECISION MAKING
Question 1 – 5 Points
Leila took a standardized test and was told that her score was in the 89th percentile. Explain clearly and in only one sentence what this means. Notes:
Percentiles are a way of describing the position of a particular score within a set of scores As per the question, I was looking for one simple sentence to explain the meaning of the statement
Ideal Answer: If Leila’s score was in the 89 percentile this means that Leila scored higher than 89% of participants in the test.
th
Question 2 – 10 Points
A gas station near the Emirates Road is revaluating its gasoline-fuel reorder point. The gasoline fuel level in its main tank triggers an automatic replenishment order. The daily demand faced by the station for gasoline is normally distributed with an average of 8,000 liters and standard deviation of 2,500 liters. After the automatic order is placed, the gasoline-fuel is received at the gas station in exactly 3 days. In other words, it takes three days lead time for the gasoline to be replenished after the order has been made. At what volume should the re-order point be set to ensure that the station’s chance of being out of stock during the replenishment period is limited to a probability of 5%? Notes:
Those people who did not score full points on this question usually made it more complicated than it is. ...

...and fashions appearing in the field of strategic management during the last decades, the SWOT analysis, standing for: strengths, weaknesses opportunities, and threats has enjoyed a long lasting popularity among both practitioners and researchers. The purpose of this essay is to demonstrate that SWOT analysis can be used for both businesses and individuals.
In the 60s swot analysis was invented at the Harvard business School for the purpose of analysing case studies,it was the efforts of two business policy professors ; professor George Albert Smith and professor C Roland Christensen. At Harvard in 1963 where a business policy conference was held about the SWOT analysis in which it has been thoroughly discussed and also considered as an important advance in the strategic thinking (Panagiotou 2003)
Since then the swot analysis has been hardly ever used, up until 1982 when Weihrich have first introduced the swot matrix as we all know it today.(appendix 1)
(Appendix1) (Adapted from Ghazinoory, S Et al.2011)
As shown in the matrix swot analysis is composed of four main elements
Strength, weaknesses, opportunities, and threats. The top part of the swot matrix containing strengths and weaknesses analyses the internal environment of the organisation means whatever it is happening inside the business, such...

...Contents
Assignment 1: 3
Introduction 3
Investment Objectives: 3
Risk Policy 3
Asset allocation 5
Constrains: 5
1- Cash 5
2- Maturity 5
3- Special Circumstances 6
4- Tax constrains (zakat) 6
Asset Selections: 6
Feedback & Control: 6
Assignment 2: 7
Transactions History 7
Portfolio Performance Vs. index Performance 9
1. Portfolio Performance vs. Dow Jones ETF Performance 10
Assignment 3 11
Portfolio Returns vs. Market Return 11
Assignment 1:
Introduction
Ayyad Co. is a financial institution, created by a group of five individuals investing their savings until their retirement age which is in 15 years. They decided to allocate USD 200,000 per person and then manage their portfolio by themselves to achieve their investment objectives. The purpose of this Investment Policy Statement is to establish guidelines for the Company’s investment portfolio. The statement also incorporates investment objectives that will be used for monitoring the progress of the Portfolio’s investment program.
Investment Objectives:
The investment objectives which are set by the company board of directors can be described by the following:
1- Annual absolute rate of return equal to 12%.
2- 2% higher than the composite benchmark consisting of market indexes weighted according to the expected target asset allocations stipulated by the Portfolio’s investment guidelines.
Risk Policy
1. Diversification: across and within asset classes is the primary means...

...represents a line in the 2D Cartesian space, because:
It represents a collection of infinite 2D points that satisfy the equation, namely, that make the two sides of the equation equal.
Notice a line is uniquely specified by two distinct points. If we draw infinite lines using any two distinct points in the collection, they will all coincide with one another, thereby forming one single line.
Slope: the amount X2 increases given one unit increase of X1
Intercept: the point where the line intersects with X2 axis.
Use above for Slope – great formula
Redundant Constraints – if removed will not affect the feasible region
Feasible Region – The set of all points that satisfy all constraints of the model
HW EXAMPLE
Apply Graphical analysis on the Golden Electronics problem with the correct formulation given in the
solution of Self-quiz 2. 1. Draw all the constraints 2. Identify the feasible region.
SEE HOMEWORK 1 as more example
RANGE OF OPTIMALITY
Apply the method of line of same profit on the Golden Electronics problem to identify the optimal solution graphically.
USING SOLVER
SEE HW2 FOR ADDITIONAL INFO
TREE SPANNING
SEE M3P1 for EXAMPLE
SEE M3P2 as EXAMPLE
SEE HW3
PROBABILITY
Statistics - The study of modeling uncertainty mathematically and its applications;
The conception of uncertainty is inspired by our daily observations of natural phenomena. There seem to be two components to these uncertain...

...
Quantitative Studies on Medication Adherence
Maleah Perdue
University of South Alabama
Introduction
Medication adherence is a significant issue in the health systems of today. Low medication adherence can unnecessarily increase cost of health care and the amount of admissions. According to Conn et al., inadequate medication adherence may account for up to 10% of older adult hospital admissions and may cause up to $100 billion in annual health care cost (2009). Increased medication adherence is likely linked to improved health outcomes while poor medication adherence can lead to exacerbations of disease or even fatality.
Area of Interest
The area of interest is medication adherence in adults that are living in the community. Specifically, older adults that are on multiple medications were looked at because of the increased medication adherence difficulties. There is an increased number of barriers to medication adherence with older adults including poly-pharmacy, comorbidities, vision impairment, hearing loss, and memory deficits among others.
Impact to Practice
Medication non-adherence impacts practice on a daily basis. The studies in these articles are looking to find methods that older adults use to increase medication adherence. Many different methods have a possibility of increasing medication compliance and if these methods could increase adherence the positive effect could be huge in the medical field. There would be less patients...

...CASE ONE
Two advertising media are being considered for promotion of a product. Radio ads cost $400 each, while newspaper ads cost $600 each. The total budget is $7,200 per week. The total number of ads should be at least 15, with at least 2 of each type, and there should be no more than 19 ads in total. The company does not want the number of newspaper ads to exceed the number of radio ads by more than 25 percent. Each newspaper ad reaches 6,000 people, 50 percent of whom will respond; while each radio ad reaches 2,000 people, 20 percent of whom will respond. The company wishes to reach as many respondents as possible while meeting all the constraints stated.
1. Develop the appropriate LP model for determining the number of ads of each type that should be placed.
2. Graph the constraints and identify the feasible region (clearly indicate the feasible region)
3. Solve the LP problem using e corner point method and comment on your findings.
CASE PROBLEM 1
1)
Radio Newspaper Min/Max
Cost 400 600 7200 Max
Min 1 1 15 Min
Max 1 1 19 Max
At least
2R 1 1 Min
At least
2N 1 2 Min
N ≤ 1.25R
Objective: 20 (2000) 5 (6000)
R = # Radio ads
N = # Newspaper ads
Therefore A= .20(2000) R + .5(6000) N
Constraints
400 R + 600N ≤ 7200
R + N ≥ 15
R + N ≤ 19
R ≥ 2
N ≥ 2
R, N ≥ 0
1.25 R – N ≥ 0
2)
400R+ 600N ≤ 7200 (4R + 6N ≤ 72)
R= (0, 18) N= (12, 0)
R + N ≥ 15
R= (0, 15)...

...USES OF BUSINESS INVENTORY CONTROL
Inventory management is one of the most important aspects of any business, especially those that are dealing with manufacturing of goods. Inventory management entails the receiving, processing and distributing of raw materials and finished goods. There are different reasons why firms need to use inventory management control techniques, some of the reasons are; provider better customer service, to have control of inventories, to increase productivity, and to create a better method of warehousing, just to name a few.
McDonalds uses just in time (JIT) inventory control system, this system helps them to better serve customer while minimizing cost of storage by storing a minimum amount of materials in order to match quicker service and maintain fresh taste. “Between 1999 and 2000, McDonald's had an inventory turn rate of 96.1549, incredible for even a high-turn industry such as fast food. This means that every 3.79 days, McDonald's goes through its entire inventory.” (Kennon, J., n.d) Inventory control is can help a firm provide superb services at a very minimum cost.
By controlling its inventories a firm increases the efficiency by which raw materials are handled in regard to production. When a firm has a better integration of its different departments it makes it easy for the handling of raw materials and finished goods, thus the delay between the firm and the customer is eliminated since...