Fourier-Motzkin doubt

Question

I understood how to do Fourier-Motzkin algorithm. But did not understand about the integer solution. Can we use the same method used for Simplex's integer solution, by enforcing the constrains to floor and ceil functions? Will that work or how can we approach that?

Answer 1

It is one of the advantages of Fourier-Motzkin to find integer solutions much easier. Once, the variables are eliminated, we backtrack and can thereby choose a value for each variable of the determined interval for that variable. If there is an integer value possible, pick it, otherwise, there is no integer solution.

Comments

Thanks for the clarification. I understood it.

---

One more doubt, If there is a question, then either if we use simplex or fourier will the rational solution be equal?

---

Usually not. It is not even the same for all ways you may use one of the two algorithms. Both algorithms have nondeterministic choices that may lead to different solutions.

---

Got it. Thanks for the clarification.