Operations research
Explainer
The Simplex Method: Walking Corner to Corner
With hundreds of variables you can't draw a graph. So how do we solve it?
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Lesson notes
Key points
- First, slack variables turn each ≤ constraint into an equation by measuring unused resource.
- The simplex method starts at a basic feasible solution, which is algebraically a vertex of the region.
- Each pivot moves to an adjacent vertex that improves the objective, stopping when no improving direction remains.
Takeaway: Simplex pivots vertex to vertex until Z can't improve.
Quick check: In a max simplex tableau, when is the solution optimal?
- No negative Z-row entries
- All slacks are zero
- Ratio test is tied
Slack variableBasic feasible solutionPivoting
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