In n-dim, the number of decision variables = n, the number of constraints = m

then, the number of basic variables = n, and the number of non basic variables = m

but when I use the big M method, how does the number of each variable change?

ex) Max Z = x1 + x2

Subject to x1 + 2x2 1-

-x1 + x2 5

x1, x2 0

>>> augmented form with big M method :

Max Z = x1 + x2 -Mx6

Subject to x1 + 2x2 - x3 + x6 = 10

x1 + 2x2 + x4 = 5

x1 + x5 = 5

x1, , x6 0