There are a number of considerations, and most of these are associated with the "Design RPM" of the engine, which lies somewhere between 85% and 96% of Max Permissible. As has been noted on some of the other replies, it is the MASS FLOW through the engine core that is a contributory factor to efficiency. A good thermal gradient through the engine core is needed, and the greater the thermal difference between intake and exhaust, the greater the power for each kg of fuel burnt. The limiting factor here is the max temperature that the tailpipe can withstand without becoming a liquid, (which is embarrassing, and frightens the pilots!)
Therefore it is prudent to get as much altitude as possible, where the Ambient OAT is very low, -56.5°C at ISA. The reduction in density as altitude increases, is virtually negated by the ram air effect of traveling through the air at high TAS.
Therefore, it is difficult to say exactly what altitude would be best for a 747 to get max range, but the optimum would take some of these factors, and probably a heap more that I dont know about into account.
Tailwinds