31,500 & 42,000 cells to lay in, after which time she can go around again.
That immediately falls down for the 1500 and 2000 layrates suggested, unless the queen is hunting around for cells as they become vacant, shoving in a few bees to clear out the cell and then drop in an egg as soon as possible.
The cycle for re-using cells is likely rather longer than that - reported as 24 days - and that may, of course depend on the number of drone brood which also come into play at these peak laying periods.
The OP can look up the number of cells in their particular hive format and multiply the anticipated maximum average lay-rate by say 24 or 25 (using a cycle of 25 days is easy as one can divide by 4 for the digits).
Or start with a practical number of brooding cells by subtracting honey arch, pollen frame space, corners of frames at the extremities of the nest and make a reduction for drone comb (it's not a large correction) and find the maximum lay-rate for your particular situation.
11 or 12 frames in the hive will make a considerable difference of course, as will as the material of the hive and floor type (along with the prevailing weather). So one should never rely on the absolute minimum - it will only get you into trouble with swarming, and there would certainly be fewer bees than could have been (even without swarming), had space not been constricted.
Remember, it is bees that make honey - more bees equates to more honey, in the right conditions. Swarming costs how much? Quite a lot - and is a useful exercise to calculate those losses, if the minimum happens to be too little......