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Simplex Tableau – Slack Variables
The Tableau is basically just a matrix of coefficients, which makes it a system of equations. The nice thing about systems of equations is that we can do mathematical operations on them, and because we know they share variables, one equation can provide information about another.
-5x - y + profit = 0
1x + 0y <= 250
0x + 1y <= 200
1x + 1y <= 300
Slack Variables
For each inequality constraint, we need to add a new variable, called a slack variable. The purpose of the slack variable is to change the inequality constraint to an equality constraint. This variable represents the difference between the two sides of the inequality and is assumed to be non-negative. For example, the inequalities
1x + 0y <= 250
0x + 1y <= 200
1x + 1y <= 300
become
1x + 0y + s1 = 250
0x + 1y + s2 = 200
1x + 1y + s3 = 300
By adding a slack variable for each inequality, the size of our tableau will grow, because instead of two variables, x and y, we now have 5 variables, x, y, s1, s2, and s3.