Efficiency in terms of basic and non basic variables of a LP I have a LP design for my problem(not relevant) where most of the variables gets assigned the value of 0. 
I want to scale the LP to more variables and equations, and thus want to know the contribution of basic and non basic variables in terms of time for solving the LP.
Alternately, if I add variables to an existing LP(expecting the new variables get assigned the value of 0), how much is the time compared to adding a variable which is guaranteed to be basic. 
 A: With an integer program, it is very difficult to predict the effect of adding integer variables that are highly like to take value zero in the optimal solution. Depending on both the specific model and the software used, it is possible that the presolver will fix some or all of the extra variables to zero before the root LP is solved. If the variables not removed by presolving are "unattractive", they may wind up with zero values in the node LP solutions. Carrying the extra variables will create some drag (since the solver is dealing with a larger LP relaxation), but possibly not a great deal of drag. Note that I'm saying "possible" a lot: there are no guarantees, and the only way to know is to try.
One possible approach to consider would be to solve the model without the extra variables, then add them and solve the expanded model, using the final solution from the first run as a starting solution to the expanded model. This might allow the solver to fix new variables at zero sooner. Personally, I would try solving the expanded model in one shot first, and only try this if solving the full model was taking too long.
