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Linear Programming, Business Management

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This is a chance to perhaps incorporate some of your experience, interests, and career business/management goals and ambitions within the context of an individual project paper. I want you to make-up your own problem and apply the linear programming tools and techniques we have been learning (Chapters 7 and 8). So you do not need to use real data here; instead, a reasonable and plausible objective function and constraints will suffice.

Pretend I am your boss or your client (i.e., you are a consultant). So I expect this paper to be 100% professional (neat, typed, error-free, descriptive, easy for me to read and follow, etc.) in nature. You are in college and, for most of you, English is your native language; that should be reflected in the quality of your writing (spelling, punctuation, grammar, etc.). At this point in your life and academic career this is assumed; i.e., you get no credit for writing at an acceptable level... instead, you incur severe sanctions if you do not.

Your problem will have exactly two variables (an X1 and an X2) and will incorporate a maximization (either profit or revenue) objective. You will include at least four constraints (not including the X1 = 0 and X2 = 0 [i.e., the “Non-negativity” or “Duh!”] constraints). At least one of these four must be a “=” constraint, and at least one other must be a “=” constraint; do not include any “= only” constraints. You must have a unique Optimal Solution Point; i.e., no unboundedness or infeasibility problems and no alternative optimal solutions.

You will make up the context, the particular numbers (objective function coefficient values), and the relationships (constraint equations and values) for your problem. I expect your model to be reasonable, plausible, and thoughtfully derived and explained—but not necessarily an accurate reflection of reality (i.e., you can make up the numbers).

Make sure you incorporate all of the topics we have gone over. Of course, it is clearly not good enough to just “mention and briefly define” any of these topics and leave it at that; instead, you need to incorporate each in your paper within the context of your problem/situation. Present and discuss your problem (background, objective, constraints, etc.) in “English” and then supplement that in “Math” (linear programming) language. (This is an extremely important part of your paper, and something that you will have to do a lot when you graduate and start a career.) The overwhelming majority of your paper will be written in “English,” with a bit of “Math” language stuff thrown in (as opposed to lots of “Math” language with a bit of “English” thrown in...).

Draw each constraint equation’s own individual graph. Then draw one “final” graph that includes the feasible region, the optimal objective function line (you need to actually graph it; do not just estimate where it goes!), and the optimal solution point. Perhaps the best way to draw these graphs is using a computer program such as EXCEL.

Make sure you incorporate (as discussed above) your objective function, constraints, slack and surplus values, optimal solution, optimal objective function value, sensitivity analysis, range of optimality, range of feasibility, dual prices, shadow prices, reduced costs, and anything else that we have discussed that is relevant to your project’s problem/situation.

While much of your work will be narrative, of course you should feel free to draw pictures, construct tables, use (and explain!) math equations and “math language,” etc., as you think appropriate and necessary. Re-stating some or all of your computer output in some other form is certainly ok; in fact, that is a big part of this project.

Make sure you include a page number for all pages.

Project Paper Assignment
(Linear Programming Models)


This paper is due by the last day of class. Of course, you can turn in your paper early if you so desire. No late papers will be accepted. If you get started SOON then you should have PLENTY of time to do a good job here.

My advice is to write the paper in sections, one or two at a time. In the interests of organization and reading ease, give each section a title (and maybe include some sub-titles too where appropriate). Double-space the text. Print on only one side of the paper (i.e., single-sided, not “duplex”; nothing on the back of any sheet of paper). Include a cover sheet/title page. Write your name(s) on the cover sheet only, nowhere else.

I know that you are all wondering “How long should this paper be?” Well, the answer is, “Long enough to get the job done!” I would expect most papers to be about seven to ten or so pages in length—but that is just a very general ballpark estimate. Of course in the real business world, which I want you to simulate here, there is seldom a minimum page length requirement for projects and papers. You will simply be expected to write enough to “get the job done”; no less, no more. I mean, can you imagine your boss saying something like “Have a twelve page report on my desk by Tuesday!”? Heck no; that is silly to even think about! Instead, your boss will simply want your report to be “long enough to get the job done.” Well… same deal here.

This is your chance to shine and to be evaluated in a context other than pencil-and-paper exams. Report/Project writing is a skill that you will need throughout your business career. Remember, your bottom-line mission here is to impress me with your ability to implement, incorporate, and professionally communicate your knowledge and understanding of linear programming as a business/ management tool, as opposed to a more purely mathematical and mechanical comprehension of it.

As with all of your other work, your paper will be evaluated from an absolute, not a relative, perspective. In other words, I do not grade “on the curve” by comparing your paper to the work of any other paper in this or any previous semester’s Quant Methods course—instead, your grade is based upon your adherence to all prescribed dimensions of this assignment this semester and the excellence with which you implement this assignment. Of course, everything you submit needs to be your (or you and your partner’s) work; i.e., you need to produce your own submitted work-product. See me if you have any questions as you plan and write your paper.

Work carefully and make sure you do everything I ask the way I ask you to do it. Remember, discussing and explaining your problem and your findings via sufficient incorporation (not just mere mention or token definition!) of the topics we discussed is a MAJOR part of this project and, therefore, of your grade. This is the kind of stuff you might do in your business career. If you have any questions about this assignment then you know what to do: see or otherwise contact me.

Finally, I advise you to jump on this like a dog on a bone. Write this paper in sections; you are capable of writing a few of these now. It has been my experience that the hardest thing is getting an idea and getting started... so do that stuff right away! Do a good job, follow all of my directives, and have FUN with this.

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