**Week 5 ** **Global
Competition - a Competitive Index **

__Introduction__

Through the various projects during weeks 1-4, you should have seen numerous applications of linear algebra to problems in science, engineering, business and society. While certainly not all encompassing, they may have provided reasonable exposure to what mathematical models can be used for.

This project, however, is much less about linear algebra and much more about your role in business or industry. It seeks to have you consider your potential place in the global workplace as well as the very nature of global competition.

Finally, a mathematical model is proposed, which, if implemented, would provide a mechanism for quantifying competition.

__Part One__**Who Would You Like to
Work for?**

In this part, you, as a team, must pick a company
you would like to work for. This may be *any *company at all. The
only restriction is that it is *not *a governmental agency or department;
it is part of the "private sector". It is probably a good idea
if the company in question relates to the majors of some, if not all, of
the members of your team.

Once you have decided upon a company, please include a description of the company in your project. Your description should include: product, brief history, size (employees and sales) at the least.

Additionally, you should include a list of who
you feel the *competition *of your company is.

Finally, what* jobs* have you taken with
this company (one per team member)?

__Part Two__**How do you measure
your company?**

In this part, the goal is to come up with a list
of characteristics or *attributes *which one would use to judge a
company by in terms of its ability to compete in the global marketplace.
These are also called *indicators* in some circles. Whatever term
you wish to use, as a team, you need to make a list of any criteria you
would use in comparing one company with another, where both are competing.

As a starting point, you might consider things such as : value of stock (if public), market share, revenue per employee, money spent on employee improvement, investment in new equipment or technology, quality of product (needs refinement) and so on.

Your list should include at least **7** such
attributes, with a brief discussion of why you chose each and what the
*unit *of measurement in each case would be.** No actual data** needed
here.

Now that you have a list of attributes, you have to decide, in relative terms, how important each one is. To this end, for each attribute, assign a number, called a *weight*, between 0 and 1, which indicates its relative importance. Additionally, the **total** of all your weights should add up to **one**. In your writeup, have two columns, one with the attribute and one with the associated weight. At the bottom of the second column, total them up.

So you can relate this to real life at bit more, include a brief description of the** DowJones** stock index and the** Consumer Price Index**

The sum *total *at any given instant in time
of all of the attributes you have chose, with possible weighting factors
added, is a measure of the competitive level of your company and may be
called a ** competitive index**. Since that number may look kind
of arbitrary, the usual method (such as in stock market indices) is to

__Part Three __**What Independent
Variables are There?**

From elementary calculus, especially functions,
we know that *independent* variables are those which may be set to
any value within a permissible domain. *Dependent *variables, or output
variables, are the results of setting those independent variables.

If you are a manager within a company, then in
its simplest form, your job is to make *decisions* about the setting
of independent variables. For that reason, they are often called *decision
variables*. Examples might be: how much to spend on advertising, who
to hire and with what background, who to buy raw materials from, what information
to get from customers and so on.

In making these decisions, you hope to positively affect the indicators of your company (the dependent variables). If you spend more on advertising, you hope the market share goes up. If you pick the best supplier of raw materials, you hope the quality of your product goes up. If you spend more on salaries, you hope to hire better people, and so on. Since there is no nice functional relationship like in elementary calculus, you are not sure of what impact your choices will make - you often have to sit back and hope the desired result happens. Sometimes one goal may be met while another is not. The Florida Marlins last year had one of the highest payrolls in Major League Baseball. For that spending they won the World Series! But on the other hand, they were $30 million in the red and had to be sold.

In this section, for your particular company,
** list** what you feel are the most important decision variables.
You should have at least 5 and preferably more. In listing them, include
your reasons on why you feel intelligent choice of them should have a positive
impact on the attributes described in

__Part Four__ A
Mathematical Model

Where does all this lead? We have a number of attributes we would like to increase so that our index increases. We have a list of decision variables we can control. But it is not clear what quantitative relationship exists between the two groups. If there were, then it would be easier to pick values for the decision variables!

Here is where regression analysis (see Project #1 of Week 1 ) If one performs linear regression analysis on data from the recent history of the company, then relationships between the variables may be quantified. The upshot is that a model of the form:

**Y = AX **

can be set up where:

**Y**
= an mx1 column of dependent variables (attributes which make up the index
from **Part Two**)

**X
**= an nx1 column of independent or decision variables (from **Part
Three** )

and **A** = an m x n matrix whose
entries are defined as

a_{ij}
= effect of a one unit change in x_{j }on y_{i}

or, in elementary calculus terms, a_{ij} is the *derivative*
of y_{i }with respect to x _{j.}

The problem then becomes one of seeking to optimize the index discussed in part two by best choice of the decision variables, X. This is a project for another course!

__Conclusion__

This particular project should have caused you to have thought about your own future as it makes a contribution to a company in todays economy and world. Further, it should have pointed out that the very nature of competition can be quantified and that techniques such as those introduced in Ma 2071 might be used to analyze it. If one can productively use mathematics to better perform one's job or manage one's company, then the mathematics is useful and worthy of the time you have put in while learning it. That has been a goal of this course.

__This Project:__

You should turn in a written paper with an introduction, results for
parts 1-3, and a conclusion which summarizes what you feel you gained from
this project. Working as a team, this should not take more than a few hours.
It is not intended to. Please hand this in no later than 10:00 am on **Monday,
Feb 16.**