I had the opportunity to learn more about the Motivation I (Relentless) bonus. +10 to production means +10 to overall production. So if your economy wheel is split even 33% to each manufacturing, research, and wealth, each will receive about 3.3 to raw production.
This means that the bonus is multiplied through your buildings. It is also affected, naturally, by race bonuses; with Yor I got +12 added to my raw production.
Here are the test numbers from my capitol, setting everything to 33%:
Before Motivation I:
7.3 Raw Manufacturing -> 38.7 Total after building buffs
7.3 Raw Research -> 7.7 (no research buildings)
7.3 Gross Income -> 2.3 net
After Motivation I:
11.3 Raw Manufacturing -> 60.1 Total
11.3 Raw Research -> 11.9 Total
11.3 Gross Income -> 6.3 Net
10*1.2(Yor Productivity Bonus) = 12 Productivity. +4 to each one, though if you have the wheel set to 100% manufacturing, you will get to 10-12 (depending on civ) manufacturing, of course.
So, taking the bonus actually is a nice benefit to your capitol. With a population of 10, I went from 21.9 total raw production to 33.9, an increase of over 50%! The increase will be somewhat less significant at higher populations, but still very useful.