1. StillWater Mining Company
a)
Interest Rate12%
Price per ounce$ 1,500.00
Cost per ounce$ 400.00
Total ounces a year10,000
Profit per ounce$ 1,100
Revenue per year$ 15,000,000.00
Cost per year$ 4,000,000.00
Profit per year$ 11,000,000.00

Every year for the next 10 years, the firm earns a profit of $11 Million. The cash flow (in $ Million) is shown below: YearTT+1T+2T+3T+4T+5T+6T+7T+8T+9
Profit11111111111111111111

Using NPV formula, we find NPV=$62,152,453.31

b) The NPVs (in $ Million) for variations in profit per ounce and interest rate are shown in table below:
8%9%10%11%12%13%14%15%
$50033.5532.0930.7229.4528.2527.1326.0825.09
$60040.2638.5136.8635.3433.932.5631.330.11
$70046.9744.9243.0141.2239.5537.9836.5135.13
$80053.6851.3449.1647.1145.243.4141.7340.15
$90060.3957.7655.35350.8548.8446.9545.17
$100067.164.1861.4558.8956.554.2652.1650.19
$110073.8170.5967.5964.7862.1559.6957.3855.21
$120080.5277.0173.7470.6767.865.1262.5960.23
$130087.2383.4379.8876.5673.4570.5467.8165.24
$140093.9489.8586.0282.4579.175.9773.0370.26
$1500100.6596.2792.1788.3484.7581.3978.2475.28

2. Savings for Future Expenditures

Interest Rate8%
Current College Tuition$ 40,000
Annual growth rate of tuition5%
Time of first college payment (yrs)6
Time of last college payment (yrs)9
Annual growth rate of investment6%
Time of last investment (yrs)9

a) The cash flow of tuition (in dollars) is shown below:
Year0123456789
Tuition------53,60456,28459,09862,053
To cover the tuition expenses she has to invest something today which if it grows at 6% every year for 9 years, provides the same NPV as the NPV of the tuition payment. Thus the present value at 0 is the initial investment. Using NPV and cash flow formula, where C_i is cash flow of tuition, and A initial investment: NPV(8%,9)=∑_(i=0)^9▒〖...

...St. Thomas University
School of Business
BUS 533 Quantitative Methods forBusiness
Dr. Maria Dolores Espino
Office: O’Mailia Hall Rm. 118
Tel: (305) 628-6791
E-mail: Mespino@stu.edu
Text :
Nagraj Balkrishnan ,Barry Render, and Ralph M. Stair Jr., ManagerialDecisionModeling with Spreadsheets Prentice Hall, 2007.
Course Overview :
Quantitative methods are used in business to aid managers and leaders in making decisions. The purpose of this course is to provide students with a comprehensive working knowledge of the quantitative methods, techniques and skills necessary for the application of concepts in learned in other MBA courses. During this course student will focus on, forecasting techniques, linear regression, project scheduling, queuing theory and linear programming. Students will learn to solve realistic problems using EXCEL and other computer- aided tools.
.Course Objectives:
• To provide students with a foundation in quantitative methods and techniques commonly used in business decision-making.
• To provide students with the ability to analyze data and models, and present results in charts, graphs, and other numerical methods.
• To introduce students to computer-aided tools which enhance and facilitate the quantitative analysis process and provide them with the skills to solve quantitative problems using Microsoft Excel and other software....

...MS5313 ManagerialDecisionModeling
Part I: Chapter 1 Describing Data with Graphical Methods
Exercises
Multiple Choice Questions:
Identify the letter of the choice that best completes the statement or answers the question.
1. Which of the following is most likely a population as opposed to a sample?
a) respondents to a newspaper survey.
b) the first 5 students completing an assignment.
c) every third person to arrive at the bank.
d) registered voters in a county.
D
2. Which of the following is most likely a parameter as opposed to a statistic?
a) The average score of the first five students completing an assignment.
b) The proportion of females registered to vote in a county.
c) The average height of people randomly selected from a database.
d) The proportion of trucks stopped yesterday that were cited for bad brakes.
D
3. To monitor campus security, the campus police office is taking a survey of the number of students in a parking lot each 30 minutes of a 24-hour period with the goal of determining when patrols of the lot would serve the most students. If X is the number of students in the lot each period of time, then X is an example of
a) a categorical random variable.
b) a discrete random variable.
c) a continuous random variable.
d) a statistic.
B
4. Researchers are concerned that the weight of the average American school child is increasing implying, among other things, that children’s clothing...

...Linear programming is a modeling technique that is used to help managers make logical and informed decisions. All date and input factors are known with certainty. Linear program models are developed in three different steps:
Formulation
Solution
Interpretation
The formulation step deals with displaying the problem in a mathematical form. Once that is developed the solution stage solves the problem and finds the variable values. During the interpretation stage the sensitivity analysis gives managers the opportunity to answer hypothetical questions regarding the solutions that are generated.
There are four basic assumptions of linear programming and they are as follows:
Certainty
Proportionality
Additivity
Divisibility
Linear programming is the development of modeling and solution procedures which employ mathematical techniques to optimize the goals and objectives of the decision-maker. Programming problems determine the optimal allocation of scarce resources to meet certain objectives. Linear Programming Problems are mathematical programming problems where all of the relationships amongst the variables are linear.
Components of a LP Formulation are as follows:
Decision Variables
Objective Function
Constraints
Non-negativity Conditions
Decision variables represent unknown quantities. The solutions for these terms are what we would like...

...TAXONOMY OF DECISIONMODELING A. MODELS: 1. DETERMINISTIC vs PROBABILISTIC 2. LINEAR vs NONLINEAR 3. UNCONSTRAINED vs CONSTRAINED 4. CONTINUOUS vs DISCRETE 5. SINGLE OBJECTIVE vs MULTIPLE OBJECTIVES B. ANALYSIS: 1. SOLUTION vs SIMULATION SOLULTION METHODS: a. TOTAL ENUMERATION b. ALGEBRAIC c. CALCULUS d. ALGORITHM e. HEURISTIC C. RESULTS: 1. OPTIMIZATION vs DESCRIPTIVE 2. GENERAL CASE vs SPECIFIC CASE
Page 1 of 4
TAXONOMY OF DECISIONMODELING (With Descriptions) A. MODELS: 1. DETERMINISTIC vs PROBABILISTIC Sometimes called “certainty” vs “uncertainty.” In deterministic models, parameter values are assumed to be known values, i.e., constants. In probabilistic models, parameter values are not known with certainty and are therefore represented by probability distributions. 2. LINEAR vs NONLINEAR Linear models are characterized by linear functional relationships, i.e., y = 2x “Linear” implies both “proportionality” and “Additivity.” Nonlinear models are characterized by nonlinear functional relationships, i.e., y = 3x2 or y = 5/x, or y = 7x1x2 3. UNCONSTRAINED vs CONSTRAINED Unconstrained models have no restrictions on the values of the solution variables. Constrained models have certain restrictions on the values of the solution variables, i.e., x ≤ 40, or x1 + 2x2 ≤ 300. 4. CONTINUOUS vs DISCRETE Sometimes referred to as “real” variables vs. “integer” variables. Continuous models contain continuous functional...

...Modeling, decision making, and optimization
In practical life, we have to continually make decisions. Making decisions are required for solving problems so that we can increase our opportunities and make life much easier and beneficial. There are many alternatives for making decisions, but making a rightful decision is a harder task. Evaluating these alternatives and choosing the best course of action represents the main essence of decision analysis.
For analyzing various decision alternatives, we have to make models.
Model
Physical
Mathematical
Visual
Mental
A model is an abstract, physical, or visual simplified replica with all features of a real object or situation.
A mathematical model is a model, which uses mathematical relationships to describe or represent an object or decision problem.
Benefits of modeling
Models are beneficial, because it is a simplified version of real object or situation, and useful to understand the real object or situation as long as it is valid. A valid model is that model, which represents the accurately the necessary characteristics of the object or problems being studied.
Models help to gain understanding about the real object or a situation, and thus help in decision-making....

...Economics for ManagerialDecision Making
Dannielle Strupler
ECO - 561 Economics – Puerto Rico
University Of Phoenix
September 18, 2012
Dr. Wanda Marrero, Ph.D.
Economics for ManagerialDecision Making
Decision making is amongst the main functions of managers within the business world today; even more particularly during these times of economic crises. Decisions such as pricing strategies targeted to particular market models of monopoly, oligopoly, monopolistic competition, and perfect competition, may help maximize revenues and profits. Also making the right choice when investing in technology, research and development, and marketing tactics can deeply impact a business’ profits and ultimately, its success or failure (McConnell & Brue, 2008).
Pricing and Non Pricing Strategies
Pricing tactics across the different markets have a strong impact on profits; decisions regarding pricing are strongly tied to the type of market being run. For instance, in a monopolistic market an increase in price will be followed by a decrease in demand. Given the fact that the product may not be trusted by consumers a highly priced article will create a negative effect on demand. Even though in this type of...

...essay will describe the concept of managerialdecision-making. It will look specifically at the ‘Rational Decision-Making Model’, exploring the shortcomings of this approach, and will suggest possible ways a manager could overcome these issues when striving to make a rational decision that will bring benefit to an organisation. Throughout this essay, empirical research and examples from academic literature will be presented to illustrate the discussion.
Decision-making is arguably the single most important process in an organisation, being a basic task at all managerial levels. (Heraclious 1994) Rational Decision Making can be defined as choices that are consistent and value maximising within specified constraints. (Bergman, Coulter, Robbins & Stagg 2008) The ‘Rational Decision-Making Model’ is a structured process for essentially making a logically sound decision. The model is made up of a series of steps, with the details often varying, but generally including; recognition of the decision requirement, diagnosis and analysis of causes, development of alternatives, selection of alternative, implementation, evaluation and feedback. (Heraclious 1994) A person making a rational decision would be logical, fully objective, and would strive to select an alternative that maximises the likelihood of achieving their goal....

...Chapter 6 – ManagerialDecision Making
Types of Decisions and Problems
A decision is a choice made from available alternatives. A decision making is the process of identifying problems and opportunities and then resolving them.
Management decisions typically fall in one of the following categories: programmed and non-programmed. A programmed decision is a decision made in response to a situation that has occurred often enough to enable decision rules to be developed and applied in the future. A non-programmed decision is a decision made in response to a situation that is unique, is poorly defined and largely unstructured, having important consequences for the organization. One of the primary differences between programmed and non-programmed decisions relates to the degree of certainty or uncertainty that managers deal with in making the decision. Every decision situation can be organized in a scale according to the availability of information and the possibility of failure; the four positions in the scale are certainty, risk, uncertainty, and ambiguity:
• Certainty: this is the situation in which all the information the decision maker needs is fully available.
• Risk: a situation in which a decision has clear-cut goals and good information is...