A Summary of the Simplex Method
(standard maximizing problem)

A standard maximizing problem

Each constraint becomes an equation with the introduction of a slack variable.
The objective function is rewritten as an equation with all the variables on the left and a zero on the right.
A matrix is written that records the coefficients/constants of these equations.
Don't ever forget that each row of the matrix represents an equation.

The entering variable (a column) is determined by the largest negative indicator in the bottom ( z ) row.
The quotients are formed using the right-hand side constants and the numbers in the column identified above.
The leaving variable is determined by the smallest positive quotient.
The pivot is the number in the entering variable column and leaving variable row.
Use the pivot row to reduce the pivot column (Gauss-Jordan).
Repeat until no negative indicators remain or it is apparent that no solution exists.