##### 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 X…

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.