# What means binding in equilibrium ?

what means "binding in equilibrium" ?

hi there,
im a german student and ive come across a phrase that is:
(2) and (5) are binding in equilibrium, and (3) and (4) are slack.

2,3,4,5 are given equations, but
can anyone explain that to me, so i can, without any knowloedge of the special mathematic vocabulary in english, translate it myself?
i know what an equilibrium is, but the rest i dont, specially not the context.

PLEASE help!
THX

## Answers and Replies

tiny-tim
Science Advisor
Homework Helper
Welcome to PF!

Hi Schreiber! Welcome to PF! hi there,
im a german student and ive come across a phrase that is:
(2) and (5) are binding in equilibrium, and (3) and (4) are slack.

2,3,4,5 are given equations, but
can anyone explain that to me, so i can, without any knowloedge of the special mathematic vocabulary in english, translate it myself?
i know what an equilibrium is, but the rest i dont, specially not the context.

PLEASE help!
THX

hmm … this looks as if it comes from OR, or linear programming.

I think the difference is between binding constraints (or equations) and slack constraints (or inequations) …

an equation with = is binding, but if it has < or ≤, it is slack …

and a slack (in)equation can be turned into a binding equation by inserting a "slack variable" (which personally I'd call a "dummy variable") …

for example, from http://en.wikipedia.org/wiki/Slack_variable
By introducing the slack variable y ≥ 0, the inequality Ax ≤ b can be converted to the equation Ax + y = b
… where (I think ) Ax ≤ b is slack but Ax + y = b is binding.

see also http://en.wikipedia.org/wiki/Linear_programming#Augmented_form_.28slack_form.29