Production =\= Manufacturing
The 3 windows at the bottom of your Planet screen show Manufacturing\Research\Wealth
Production is generally not shown except as Raw in the tooltips of these 3.
Production is divided by the Wheel to those 3 things. I believe you understand this.
The equation for Production is:
[production] = (1 + [production multipliers])*([flat production bonuses] + 2 *[population]^0.7)*f([approval])
production multipliers and flat production bonuses
are not shown in the tooltips yet but are made by things like the Government techs in the research window.
f([approval]) is roughly linear from 100% approval being 0.25 to 0% approval being -0.25
I hope this helps you. I have tried to keep this simplistic since I understand language barriers.
Thanks to Joeball for the equation.