A slack variable
A) is the amount by which the left side of a ≥ constraint is larger than the right side.
B) is the amount by which the left side of a ≤ constraint is smaller than the right side.
C) is the difference between the left and right side of a constraint.
D) exists for each variable in a linear programming problem.

Question

Quizplus · Accepted Answer

A slack variable is added to an inequality in the standard form of a linear programming problem to convert it into an equality. In the case of a ≤ constraint, the slack variable is the amount by which the left side is smaller than the right side, so B is the correct option. Option A is incorrect because it describes a surplus variable, which is used for ≥ constraints. Option C is incorrect because it describes the slackness condition, which is a property of the optimal solution and not a variable. Option D is incorrect because not every variable necessarily has a slack or surplus variable associated with it.

A Slack Variable