Not to detract from what was written before as it sounds familiar-ish from way back.
Can a simplified visual model be related to this?
Simply put the aircrafts polar curve, min. sink (best endurance) ~Vx and L/D max. (best range) being always a higher IAS/TAS than Vx although usually Vy is faster than L/D max. to accomodate other issues, cooling, thrust/power curve etc.
Gets a bit messy linking turbine best range speed with L/D max due to the nasty habit turbines have of consuming 1/2 their fuel just to keep running.
If I've got this wrong I hope someone will straighten me up.