Your throat is dry, and you want the last cough drop in the box to last a long time in your mouth. What should you do?

The cough drop shall be taken in such a way that it has high surface-to-volume ratio

Explanation:

In order to maintain a large surface-to-volume ratio, the cough drop must be taken in a way that its entire volume is higher than the surface area occupied by it. This can be achieved only by taking cough drop all at once so that its volume remain higher than the surface area.

The higher is the surface-to-volume ratio, the lower is the dissolution of any substance, thus the cough drop with high surface-to-volume ratio will dissolve slowly and hence it would last longer than usual.

Keep the cough drop whole. This maintains the largest surface-to-volume ratio, and slows the dissolution of the cough drop.