Final answer:
The number of slack variables equals the number of 'less than or equal to' constraints in a linear programming problem. To name them, we assign a variable such as s1, s2, etc. These slack variables are then added to the constraints to convert them into linear equations.
Step-by-step explanation:
To determine the number of slack variables and name them, first, we need to examine each constraint in the linear programming problem. Slack variables are additional variables that are added to inequalities to turn them into equalities (linear equations). For each 'less than or equal to' constraint, a slack variable is added to convert it into an equation.
For instance, if we have a constraint like x + 2y ≤ 10, we would add a slack variable (let's call it s1) to turn it into an equation: x + 2y + s1 = 10. If there are 'greater than or equal to' constraints, we would add surplus variables and possibly artificial variables, but for simplicity, let's assume we only have 'less than or equal to' constraints.
Next, using the slack variables, we convert each constraint into a linear equation by adding the slack variable to the left-hand side of the inequality so it becomes an equality. After identifying all the constraints, you should end up with the same number of slack variables as constraints, each corresponding to one constraint.
Overall, the process of converting constraints into linear equations using slack variables is a key step in setting up the standard form for linear programming problems.