Project Paper Assignment(Linear Programming Models)
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. Make-up your own problem and apply the linear programming tools and techniques we have been learning (Chapters 7 and 8). You do not need to use real data here; instead a reasonable and plausible objective function and constraints will suffice.
Pretend your instructor is your boss or your client (i.e. you are a consultant). Your paper should be 100% professional (neat typed error-free descriptive easy 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 X1and 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. Your model should be reasonable plausible and thoughtfully derived and explainedbut 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 equations 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 graphsis 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 projects 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 soonthen you should haveplenty 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 onlyone 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 lengthbut 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.
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 semesters Quant Methods courseinstead 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 partners) work; i.e. you need to produce your own submitted work-product.
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.

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