Problem Formulation Examples

Optimization · Axiom Academy

EXAMPLE Problem Formulation Examples Learn how to translate real-world problems into mathematical optimization models A company produces two products A and B. Each unit of A requires 2 hours of labor and yields 30 profit. Each unit of B requires 3 hours of labor and yields 50 profit. The company has 120 labor hours available. Question: How should they allocate production to maximize profit? Excellent work! You've completed this optimization problem formulation. Here's what we learned: Decision Variables: These represent the choices you can make. Always define them clearly with units. Objective Function: Express what you want to optimize (maximize profit, minimize cost, etc.) as a mathematical function of your decision variables. Constraints: Translate limitations and requirements into mathematical inequalities or equations. Don't forget non-negativity constraints when variables represent physical quantities. Problem Classification: This was a linear programming (LP) problem because both the objective and constraints are linear functions of the decision variables. Master these four steps and you'll be able to formulate any optimization problem systematically!

This is the written version of the interactive lesson above. See the full Optimization course.