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Consider any modern jetliner (narrow-body and widebody separately) in a standard 2 or 3 class configuration. If somehow only first-class or business-class passengers bought seats, would that plane be impossible to fly because all the weight is focused up front? And since they are premium-class they can't be moved aft for load-balancing.

If this is (practically) impossible, then doesn't that suggest there is a minimum number of economy passengers required as "ballast" for every premium passenger?

I suspect one answer might be that the flight wouldn't be profitable anyway with few-to-none economy seats sold, so it would be cancelled. But let's suppose in that case the aircraft needed to be flown anyway because it was required to be at the destination airport, profitably or not. Doesn't that suggest there is a maximum "premium-only" passenger count that would actually be less than the number of premium seats? I.e they would have to tell some premium passengers "sorry you're bumped, or you can go to economy" despite the plane being 80% empty?

It is much more difficult to load a plane so that the center of gravity ends up being too far forward than too far aft.
Excessive weight forward can almost always be counteracted by increased trim on the stabilizer.

When small GA planes crash due to Balance, its almost always too much rear-weight, not too much forward-weight.

Especially in the case you describe, the pax probably have luggage, and the luggage can be loaded in the rear of the plane for balance.

As has been noted in the previous answer and comments to date, you can compensate (if you need to) for a first class loaded with pax but with the rest of the cabin empty by putting the pax bags in the rear.

Generalized statements like the above sometimes have exceptions, but I'd be surprised if that one did.

I worked a weight and balance for a 747-400F putting the equivalent of 72 pax at 200 lb each in the forward quarter of the airplane. That moved the c.g. %mac from 30.8 to 22.4, still well aft of the zero fuel weight forward c.g. limit of 16.0.

Then I put in 200000 lb of fuel, 2000 for taxi, 170000 burn. The forward c.g. limits for the taxi envelope, takeoff envelope, and landing envelope were still not exceeded.

The moral of the story thus far is that passengers take up a lot of room, but they don't weigh much relatively speaking.

However, when I loaded 350000 lb of fuel, it put the taxi c.g. at 10.9, just forward of its limit of 11.0, and the takeoff c.g. at 10.8, just forward of its limit of 11.0. I fixed the out of limits condition by putting in 50 lbs of baggage for each pax, splitting the weight between K48L and K48R, the two aftmost lower cargo ULD positions.

If you want to take a look at the test load with the 350000 lb of fuel but before adding in the bags, go to https://terryliittschwager.com/WB/index.php. Once there and after dismissing the initial message window, select the SERVER Load at the top of the list. It has a false date of 2222-01-08 to keep it at the top.

You can fix the out of limits condition by scrolling down to K48L and K48R and putting 1800 lb in each.

The passengers don't weigh enough to seriously affect the weight & balance, especially since there are usually less than 20 people in first class. I was on a Pan Am flight soon before its demise, and there were maybe 10 people on the plane. They invited everyone up to first class, after all the baggage had been loaded, so there was no compensating for the shifted passenger load.