Ok, Let's take an example (number may be off, but formula will be correct). On you planet you have:
- a colony base producing 20 manufacturing point and 20 research point
- a research center producing 10 research point
- 2 factory producing 8 manufacturing point each.
So for the planet, you have :
- 20 + 2*8 = 36 manufacturing points
- 20 + 10 = 30 research points
If you set :
100 % spending split 30% for military, 40% for social and 30% for research, you will procduct:
military: 100%*30%*36 = 1 * 0.3 *36 = 10.8 = 10 BC
social : 100%*40%*36 = 1 *0.4 * 36 = 14.4 = 14 BC
research: 100% * 30% * 30 = 03 * 30 = 9 BC
Total spending: 10 + 14 + 9 = 33 BC
If you set:
75% spending, split 40% military, 40% social and 20% research, you will product:
military = 75%*40%*36 = 0.75 * 0.4 * 36 = 0.3 * 36 = 10.8 = 10 BC
social = 75% * 40% * 36 = 0.75 * 4 *36 = 0.3*36 = 10.8 = 10 BC
research

75% * 20 % * 30 = 0.75 * 0.2 * 30 = 0.15 * 30 = 4.5 = 4 BC
Total spending : 10 + 10 + 4 = 24 BC
Any question?