Lessons from Lemonade

core idea: when you have multiple ways to achieve the same result, prefer using the less flexible resource. $1.$ $5$ bills are flexible (help with $10$ and $20$ customers)

$2.$ $10$ bills are inflexible (only help with $20$ customers)

$3.$ Greedy choice: spend inflexible resources first. This pattern appears in many problems: when allocating resources, save the versatile ones for later. This principle applies beyond currency: in scheduling, resource allocation, and task assignment. Preserve flexibility whenever possible.