Simplex Algorithm

Question

For the Simplex Algorithm problem in the exam, before pivoting the variable do we need to check the below condition always?
Wouldn't the variables X0 and X1 if provided with limits from -inf to +inf, be sufficient to pivot for at least the first two iterations, without checking the condition?
 

Answer 1

The expression ensures that xj has room to move in a direction that will allow us to change the value of yi which currently violates one of its bounds. If xj is unbounded, i.e., has no bounds, then we can obviously choose it and don't have to check the above condition .