Slack variables

Slack variables are tools used in optimization, particularly in linear programming, to help transform inequalities into equalities. When constraints are expressed as limits (e.g., "no more than 10"), slack variables measure the difference between the maximum allowed and the actual amount used. For example, if a resource limit is 10 and only 7 is used, the slack variable would be 3, indicating unused capacity. By incorporating slack variables, we can better analyze and solve complex problems, ensuring that all constraints are accounted for in a manageable way.