Question

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. Your model should 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.

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