Operations research
Why?
Why Simplex Needs Slack Variables
Why does the simplex method add slack variables to constraints?
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Lesson notes
Key points
- Because simplex works with equations, but most LP constraints are inequalities like 2x plus y less than or equal to 10.
- Because a slack variable measures the unused resource, turning each inequality into an exact equation with s at least zero.
- Because setting all decision variables to zero leaves slacks equal to the right-hand sides, giving a ready starting corner.
Definitions
- Slack variable
- A non-negative variable added to a ≤ constraint equal to the unused amount of that resource.
Takeaway: So slacks make standard form and hand simplex its first corner.
Quick check: In the first simplex tableau, which variables are basic?
- The decision variables
- The slack variables
- The objective coefficients
With decision variables at zero, slacks equal the right-hand sides.
Equations neededUnused resourceInitial basis
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