Operations research
Why?
Why Simplex Needs Slack Variables
Why does simplex add slack variables to every ≤ constraint?
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Lesson notes
Key points
- Because simplex works with equations, not inequalities, so each ≤ constraint must become an equality first.
- Because the slack measures unused resource, like spare truck hours at a mine in Tarkwa, it is never negative.
- Because setting all decision variables to zero leaves slacks equal to the right-hand sides, they give a ready starting basis.
Takeaway: So slacks turn limits into equations and hand simplex its starting corner.
Quick check: In the first simplex tableau of a ≤ problem, which variables are basic?
- The decision variables
- The slack variables
- The objective coefficients
With decision variables at zero, slacks equal the RHS and form the starting basis.
Equations neededUnused resourceInitial basis
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