(Linear Programming Models)This is a chance to perhaps incorporate some of your experience, interests, and career business/managementgoals and ambitions within the context of an individual project paper. Make-up your own problem and applythe linear programming tools and techniques we have been learning (Chapters 7 and 8). You do not need to usereal 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., youget 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 (eitherprofit or revenue) objective. You will include at least four constraints (not including the X1 ? 0 and X2 ? 0[i.e., the âNon-negativityâ or âDuh!â] constraints). At least one of these four must be a â?â constraint, and atleast one other must be a â?â constraint; do not include any â= onlyâ constraints. You must have a uniqueOptimal 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 therelationships (constraint equations and values) for your problem. Your model should be reasonable, plausible,and thoughtfully derived and explainedâbut not necessarily an accurate reflection of reality (i.e., you can makeup the numbers).Make sure you incorporate all of the topics we have gone over. Of course, it is clearly not good enough to justâmention and briefly defineâ any of these topics and leave it at that; instead, you need to incorporate each inyour paper within the context of your problem/situation. Present and discuss your problem (background,objective, constraints, etc.) in âEnglishâ and then supplement that in âMathâ (linear programming) language.(This is an extremely important part of your paper, and something that you will have to do a lot when yougraduate and start a career.) The overwhelming majority of your paper will be written in âEnglish,â with a bitof âMathâ language stuff thrown in (as opposed to lots of âMathâ language with a bit of âEnglishâ thrown in).Draw each constraint equationâs own individual graph. Then draw one âfinalâ graph that includes the feasibleregion, 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 asEXCEL.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 yourprojectâs 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 âmath language,â etc., as you think appropriate and necessary. Re-statingsome 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. MGMT 206 Management Science 2 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 latepapers 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 readingease, give each section a title (and maybe include some sub-titles too where appropriate). Double-space thetext. Print on only one side of the paper (i.e., single-sided, not âduplexâ; nothing on the back of any sheet ofpaper). Include a cover sheet/title page. Write your name(s) on the cover sheet only, nowhere else.I know that you are all wondering âHow long should this paper be?â Well, the answer is, âLong enough to getthe job done!â I would expect most papers to be about seven to ten or so pages in lengthâbut that is just a verygeneral ballpark estimate. Of course in the real business world, which I want you to simulate here, there isseldom a minimum page length requirement for projects and papers. You will simply be expected to writeenough to âget the job doneâ; no less, no more.This is your chance to shine and to be evaluated in a context other than pencil-and-paper exams. Report/Projectwriting is a skill that you will need throughout your business career. Remember, your bottom-line mission hereis to impress me with your ability to implement, incorporate, and professionally communicate your knowledgeand understanding of linear programming as a business/ management tool, as opposed to a more purelymathematical and mechanical comprehension of it.As with all of your other work, your paper will be evaluated from an absolute, not a relative, perspective. Inother words, I do not grade âon the curveâ by comparing your paper to the work of any other paper in this orany previous semesterâs Quant Methods courseâinstead, your grade is based upon your adherence to allprescribed dimensions of this assignment this semester and the excellence with which you implement thisassignment. Of course, everything you submit needs to be your (or you and your partnerâs) work; i.e., you needto produce your own submitted work-product.Remember, discussing and explaining your problem and your findings via sufficient incorporation (not justmere mention or token definition!) of the topics we discussed is a MAJOR part of this project and, therefore, ofyour grade. This is the kind of stuff you might do in your business career.
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