### LP6

## Linear Programming Sensitivity Analysis

Recall the Acme Bicycle Company example:

**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

We will look at the sensitivity of the solution that we found in the previous examples. We will be answering this question: is the optimum solution sensitive to a small change in one of the original problem coefficients?

Before the animation, look over the following output obtained from the LINDO LP solver. The animation will discuss the ranges boxed in red in particular.