### LP3

## Using the Simplex Tableau

The simplex method is a simple and elegant algorithmic engine for solving linear programs. This example demonstrates its mechanics. The animation solves the Acme Bicycle Company example using the simplex tableau. The Acme Bicycle Company formulation is repeated below.

**Variables:**

- x₁: mountain bikes to produce (bikes/day)
- x₂: racers to produce (bikes/day)

**Variable non-negativity:**

- x₁ ≥ 0, x₂ ≥ 0

**Objective Function:**

- Maximize daily profit ($/day): Max Z = 15 x₁ + 10 x₂

**Constraints:**

- Mountain bike production limit (bikes/day): x₁ ≤ 2
- Racer production limit (bikes/day): x₂ ≤ 3
- Metal finishing machine production limit (bikes/day): x₁ + x₂ ≤ 4