The Simplex method, with pivots and slack variables, etc., is basically a way of exploring the possible space of solutions. If you plot the boundaries of your problem, you get a quadrilateral in the first quadrant. The function you're trying to maximize has a set of equal value lines that are all parallel to each other, and extend throughout all of the xy plane. Your maximum will be on one of the equal value lines that intersect a vertex of the boundary quadrilateral. To first get a feel for the problem, you can just test the vertices of the quadrilateral (i.e., (x,y) = (0,0), etc.) on your maximization function x+2y (here = 0), to see what the answer to your problem will be.