Basic Columns In Simplex

Question

On the following note it says that if a non basic column has no positive coefficient so this is the case of unboundedness.

What non basic column refer to?

Answer 1

If you mean related to the link you shared, it's talking about the initial tableau on page 4, where column $x_2$ has all negative numbers.

If you are asking as if why this is the case, just take a look at the example's formulation. $x_1, x_2 >=0$. $x_2$ has a positive coefficient in the maximization objective function, but negative coefficients in all the constraints. You can increase $x_2$ as much as you want without violating any constraint and keep increasing your objective function.

If you are still wondering about the reasoning of it, well, because if you select $x_2$ to enter the basis, all your pivot elements are negative (they need to be positive for you to enter). So, what happens when they are negative? There is no cap for you to stop increasing your variable. You can incrase it as much as you want.