In general, you cannot use any variable for pivoting, and of course you should only choose those that do not yet fulfill the constraints. If some yi violates the bound, you need to find a non-basic variable xi that can be modified such that yi has a chance to fulfill the constraints. What that means precisely is formulated on slide 64.

After this, the situation changes. Maybe the other constraint is then also fulfilled, you need to evaluate the new situation from a fresh point of view and cannot really make a long-term plan.