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 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.