Chapter 4: Linear Programming
Optimising profits when facing multiple resource constraints.
About this Lecture
In Chapter 3, we solved problems with one shortage. But what if you are short on labour AND materials at the same time? This lecture introduces Linear Programming, a mathematical method to find the optimal product mix when you have multiple constraints. We will cover the graphical method, iso-contribution lines, and solving simultaneous equations.
Study Guide Highlights
1. The 3 Pillars of Linear Programming
- Variables: What are we making? (Usually Let x = Product A, y = Product B).
- Objective Function: What is the goal? (Usually Maximise Contribution: C = ax + by).
- Constraints: What stops us? (Resource Used ≤ Resource Available).
2. The 6-Step Approach
- Define variables.
- State Objective function.
- Formulate Constraints (don't forget non-negativity: x,y ≥ 0).
- Graph the feasible region.
- Solve for the optimal point.
- Answer the specific question asked.
3. Exam Tips & The "Golden Rule"
The optimal solution will ALWAYS be at one of the corners (vertices) of the feasible region. You often need Simultaneous Equations to find the exact coordinates.
Remember, we assume costs and prices are constant. No bulk discounts or overtime rates are included in basic LP models.
Chapter Resources
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