I have a page with a very detailed description of the simplex algorithm and it seems that it lacks the conditions of the stop. The site is in Polish so I will have to use another simpler page to explain what I mean. Please check if I understand correctly?

http://www.phpsimplex.com/en/simplex_method_example.htm

1) We check if there is a number less than zero in the row (Z). If it does not exist, we have the first stop condition, that is the maximum of the function that can be read from the P0 column.

2) Then we check whether there is a value greater than zero in the selected column for the smallest value in the selected row (Z) (in the example it is P1). If it is not there, then there is no solution because the function tends to infinity.

In which place and how to check if the function has no solutions because the domain is an empty set?