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If the sea level was 30000 feet, all land would be submerged and no beaches would exist.

If the sea level was -30000 feet, no sea would exist and there would also be no beaches.

The beach area maximizing sea level must be between these values. What is it?

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    $\begingroup$ are you asking at what sea level we will have the longest shoreline,this is not the same as beach area if you remove all the water the "beach area" will be maximized. $\endgroup$ – trond hansen Mar 3 at 6:26
  • $\begingroup$ There are inland beaches at lakes. Do you mean beach, or do you mean coastline? Are you aware of the coastline paradox? $\endgroup$ – gerrit Mar 3 at 9:07
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There are multiple ways one can look into this. For example, one simple way of increasing the length of coastline and, thus the beach area, would be to expose all of continental shelf.

The shelf break, where the continental shelf ends is pretty uniform globally and is in most cases at a depth of 140 m. As such, lowering water level by this amount will produce a large increase in beach areas.

Alternatively, it might be possible to increase the overall length of the coast by increasing the water level by ~100 m. While here we lose a substantial amount of coast due to flooding of low-lying areas of continents, there will be substantial gains as well.

Such an increase firstly will create a lot of new inlets resulting in minor increase of coastal areas, but most importantly this will cause the water level to reach bases of several mountain ranges - Alps, Himalayas, Caucasus to name a few. This will create an extremely rugged coastline with ridiculous amount of fjords and bring huge increase to the coastline length.

The issue with the latter option is that I'm not sure how likely you are to have a 'beach' in a fjord environment or what exactly we should consider a 'beach' for the purposes of your question.

In reality it's a pretty complicated question and it can only be solved by sitting down with modelling of coastline length at different water levels.

EDIT: Another interesting option is to reduce water level by ~3-4 km. This will maximize the land area while maintaining water in the deep oceanic basins and at the same time the longest mountain range in the world - the mid-ocean ridge - will get exposed above sea level adding on to the overall coastal length.

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