This is for an exam rather for homework. I'm doing an optimization course, and there will be simplex problems to solve. Most (if not all) are with two variables and around two constraints. I want to find a method that will allow me to pick the base immediatelly so the whole method requires one iteration to converge to the optimal solution.
I don't have to use the Two Phase method yet because they haven't taught it yet. For now I think it's about picking random bases and testing them.
So, the question: Is there a way/trick I can immediatelly pick the right base that will lead me to the simplex method being only one iteration? (Assuming the problem is very small, such as a 2 variable problem)
I know how to do the whole simplex method, but it's time consuming for a test like this. Also, I'm studying for engineering, so I don't need to do this manually (nobody needs to!)
Use the graphical method. See, e.g., http://www.linearprogramming.info/linear-programming-graphical-method/