### LP4

## Finding the Optimum Point Graphically for a Two-Phase Linear Program

Recall the Acme Bicycle Company Example that was discussed in the notes and previous examples:

**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