Operations research
It is like…
Slack Variables Are Like Leftover Budget
A slack variable is like the change left in your pocket
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Lesson notes
Key points
- You take fifty cedis to the market, spend forty-two, and walk home with eight cedis unused in your pocket.
- In an LP, a less-than-or-equal constraint is your budget, and the slack variable is that unused change turning the inequality into an equation.
- The analogy breaks for greater-than-or-equal constraints, where you subtract a surplus variable, the amount you exceed a minimum requirement.
Takeaway: Slack is unused resource; surplus is excess above a minimum.
Quick check: What value does the slack take when a ≤ constraint is binding?
- Equal to the RHS
- Zero
- Negative
Binding means all of the resource is used, so nothing is left over.
Leftover moneySlack variableSurplus variable
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