To clarify, this is not a question about how to conduct test of optimality or about what is the test good for. Nor am I asking for mathematical proof supporting it.
I am asking specifically for definition of the test itself. Meaning, what would you say if you had to explain what the optimality test is.
I had this question on test and ,frankly, it caught me off guard.
The simplex method iteratively moves from extreme point to extreme point, until it reaches the optimal one. Each extreme point is characterized by a set of basic variables, so moving to another extreme point is like considering a new set of basic variables, more precisely, it is like getting rid of ONE basic variable and replacing it with another non basic variable.
This being said, the optimality test is easy to define. It consists in considering each potential new basic variable, and checking its impact on the objective function. Technically, this is done by computing the reduced cost of the non basic variable. For a maximization (minimization) problem, if the reduced costs of all non basic variables are negative (positive), the solution is optimal.