My textbook states "If there are no negative values in the top row of the Simplex tableau, then we have reached optimality"
That seems intuitive enough. However, I am wondering if the following, stronger statement is also true?
"We have reached optimality if and only if there are no negative values in the top row of the Simplex tableau".
Your stronger statement is true if the solution is non-degenerate. (Provided that the objective function is
maximize.)