I think most of the points necessary to solve the Ops question have now been made:
Gouli - I was assuming that the intention was to set KTAS and ALT and then (for whatever reason
) leave the setting alone whilst the aircraft flew to flameout. The fact that this would not achieve max endurance was not relevant to the OP's specification and, so far as I can see, does not make the original question invalid.
AdamFrisch - Has raised the important point that what we need to do is minimise drag in order to get max endurance and that this is achieved at Vbg or Vy. This will vary with weight but if,as AtoBsafely has suggested, we assume 2/3 of the original fuel, we won't be far off.
AtoBSafely has raised the point that we would be more efficient operating on one engine at a higher power than two engines at lower power. Would the additional drag caused by asymmetric flight outweigh the advantage and would the on-board systems feed all the fuel to the one running engine without further intervention?
AdamFrisch has also suggested that endurance is independent of altitude. Instinctively this sounds right - maybe someone can comment on whether fuel flow varies for a given KTAS (approx Vy) at different altitudes.
So the question may boil down to - what is the fuel burn, independent of altitude, on a single engine, to fly at Vbg (or Vy)at approx 2/3 of the original fuel load? Given that we start with 43,800 kg of fuel, how long will this last?