Final answer:
To maximize free time in a shared apartment, the roommate most efficient at cleaning should do the dishes while others vacuum. However, this may create feelings of unfairness, similar to trade scenarios where comparative advantages exist. Establishing a cooperative cleaning schedule could help maintain fairness.
Step-by-step explanation:
In an apartment where cleaning efficiency varies among roommates, it's important to assign tasks strategically to maximize free time. Since one roommate is 70% faster at doing dishes and 10% faster at vacuuming, they should focus on the task where they have the greatest relative speed advantage, which is washing dishes. The other roommates can be assigned vacuuming, which requires less time advantage.
However, this efficiency can lead to problems such as one roommate always getting tasks done quicker and potentially feeling burdened by the unequal distribution of labor. This scenario can result in tensions and a feeling of unfairness. In trade-related terms, this is akin to a comparative advantage where one party may be more efficient in producing certain goods or services but still benefits from trading with others to maximize overall productivity and satisfaction.
A cooperative cleaning schedule or rotation might need to be established to maintain fairness and morale within the household. Doing so can help prevent resentment and ensure that all roommates contribute to maintaining a clean living environment.