Daniel's Recipe — Limiting Ingredient Problem

Daniel has plenty of flour, plenty of sugar, and enough butter — but only 5 eggs. The eggs run out first, and when they do, no more cupcakes can be made regardless of how much of everything else is left. This is the "limiting ingredient" concept: the answer is always determined by whichever resource runs out first, not by the one you have the most of.

Limiting ingredient / bottleneck maximisation questions appear regularly in OC TS and reward students who check every resource rather than rushing to use the largest number. Students who pick 24 (from butter) have done the right calculation but stopped at the wrong ingredient. The correct approach is to calculate the cupcake cap for every ingredient and take the smallest.

The examiner is checking whether you can set up a "max output per ingredient" calculation for each resource, identify the smallest result (the bottleneck), and verify it by checking whether all other ingredients can support that number. The final verification step is essential — it confirms the bottleneck choice is correct.

A recipe or process requires multiple ingredients or resources in fixed proportions. You are given a quantity of each ingredient. The question asks for the maximum number of items that can be produced. You calculate the maximum each ingredient allows and pick the minimum — that is the bottleneck and the answer.