I was watching the lecture videos on Discrete Optimization on Coursera and I came across something I couldn't understand. A solution is feasible if the following constraints (picture below) are satisfied.
I have been wondering if it possible for the solution to satisfy the constraint yet be unfeasible like in the image below ? Is there a simple proof (pictorial) that shows why the scenario below is impossible ?
I have been thinking it through and I am wondering if the magic lies when you add the slack variables which brings the 'plots' into a higher dimension and when you solve for m variables (assuming m constraints) at that higher dimension, you are guaranteed that the solution (at the original dimension) will always be a feasible solution.
