Quota sampling is purposive sampling. Some literature suggests that quota sampling may accurately reflect the population if it is chosen based on relevant divisions in the population. The problem is that error is not predictable statistically. This technique is often used to achieve necessary variation in underrepresented sub-populations. Deadlines may effect even a well funded study.
Funding is usually an issue in sample size.
If resources cannot be devoted to this goal, there should be no survey. Any of these can increase response rate. If r and n were formed randomly, then they are functionally equal. The proportion of non-responders must be kept to such a small level that it cannot effect the equation strongly. In probability sampling, efforts to reduce sampling bias are initiated by ensuring that all members of the frame have an equal and non-zero probability of selections.