Final answer:
To maximize overall free time, the person should take on task of dishes which they are significantly faster at, while roommates vacuum. This can lead to resentment or issues with cleanliness. A trade-related analogy is specialization based on comparative advantage.
Step-by-step explanation:
When living with roommates who do not clean up after themselves, managing housework efficiently can be challenging. It is important to allocate chores in a way that maximizes the overall free time for everyone involved. Given that the person is 70% faster at doing dishes and only 10% faster at vacuuming, they should take on the task of doing dishes. This is because they can complete it much more quickly than their roommates, resulting in greater overall time savings for everyone. The roommates can be assigned to vacuum, which takes them relatively less time compared to the disparity in washing dishes.
However, this can create social and practical problems. The faster cleaner may feel taken advantage of or become resentful if they perceive that the housework is not equitably divided. There might also be issues with the level of cleanliness if the slower roommates do not clean to the same standard. A trade-related analogy would be specializing in tasks where one has a comparative advantage, similar to countries that specialize in producing goods where they are most efficient, leading to overall greater productivity and trade benefits.