Graph the four inequalities. Find the area where they ALL overlap. Determine the vertices of the solution set polygon either by inspection or by solving 2X2 systems of equations to determine the intersection points of the boundary lines.
The coordinates of at least one of the vertices of the feasible area polygon (that is the solution set of the system of 4 inequalities) will optimize the objective function, f(x,y). If two of the vertices are equally optimum, then the two vertices will be adjacent and every point on the line between them will also be optimum.
Hint: Anytime I do one of these problems, I graph the inequalities with the opposite sense given. What that does is shade in all of the areas of the plane that are NOT in the solution set, and the solution set is completely unshaded. The feasible area is then clearly displayed as a white area and you aren't forced to try to discern whether certain areas have shading from all or only some of the inequality graphs. Just make sure you annotate any graphs you turn in to your instructor for credit so that there is no confusion about what you are doing.
John
My calculator said it, I believe it, that settles it
