It would be great if we had a "Maximum range" Cruise page in the FMC.
LRC is defined as the Maximum Range reduced by 1%.
That's because we must go faster when flying into a headwind to keep the best fuel mileage.
LRC will give the maximum range with a 100kts headwind, with a very low penalty in case of a tailwind.
Typically LRC is Maximum Range speed plus 10-25kts.
In your example, a very low cost index gives a very low speed, which gets closer to Maximum Range (remember LRC is faster, and is optimized for a strong headwind.)
In other words, with a tailwind the slower you fly the longer distance you can cover with your fuel.

hope I didn't say too many b******t!