The knapsack problem is a classic optimization dilemma that can be applied to various use cases, including packing luggage for a holiday. PostgreSQL and recursive Common Table Expressions (CTEs) can help solve this problem by finding the combination of items with maximum value within a defined weight constraint. In this tutorial, we demonstrate how to create an inventory table in PostgreSQL and use recursive CTEs to find all combinations of items that fit into a luggage with a 20 capacity. The solution provides a theoretical exercise for solving the knapsack problem and can be adapted to real-world constraints.