# Simplex Method

Canonical: https://manyspace.aporia.systems/topics/simplex-method-mth-opt-235
Updated: 2026-10-13

Mathematics · Optimization · MTH-OPT-235

- Difficulty: 3 / 5
- Importance: 5 / 5
- Study time: 4–8.5 h

tableau, pivoting, degeneracy, two-phase method

## Why it matters

Choosing the best under constraints; central to operations research, ML training, engineering design and business resource allocation.

## Where it is used

Supply chains, pricing algorithms, portfolio optimization, neural network training, logistics, ad auctions.

## How you know you have learned it

Produce working code/model + convergence/validation/error analysis.

## What you need first

- [Gaussian Elimination](https://manyspace.aporia.systems/topics/gaussian-elimination-mth-linalg-155) (required)
- [3D Coordinates & Vectors](https://manyspace.aporia.systems/topics/3d-coordinates-vectors-mth-multc-168) (required)

## Resources

- Introduction to Linear Programming — Bertsimas & Tsitsiklis
- Convex Optimization (Boyd & Vandenberghe) — Boyd & Vandenberghe
- Convex Optimization (Boyd & Vandenberghe) — Boyd & Vandenberghe