A bakery's cookie recipe uses flour, sugar and butter in the ratio 5 : 3 : 2 by weight. The bakery has 40 kg of flour, 30 kg of sugar and 12 kg of butter in store. The greatest weight of the mixture (in kg) it can prepare is:

Butter is 2 parts out of 10, so 12 kg of butter supports a batch of $12\times 10/2=60$ kg, which needs 30 kg of flour and 18 kg of sugar — both in stock. The butter runs out first and caps the batch. (Working from the flour, $40\times 10/5=80$ kg, or from the sugar, $30\times 10/3=100$ kg, ignores the ingredient in shortest supply. 82 kg is merely everything in the store weighed together, which is not a mixture in the required ratio.)