How are slack variables introduced in the simplex method as described in the chapter?

Slack variables are introduced in the simplex method to convert inequalities into equations. Each inequality is rewritten by adding a slack variable, which represents the difference between the left-hand side and the right-hand side of the inequality, ensuring that all constraints have a positive right-hand side constant term.

In the simplex method, the first step is to express all inequalities as equations by introducing slack variables. For instance, an inequality like —x + 2y < 6 is transformed into an equation by adding a slack variable, resulting in —x + 2y + w1 = 6, where w1 is a non-negative slack variable. This process allows the constraints to be represented in a form suitable for the simplex tableau, which is essential for solving linear programming problems.