Miner to Furnace ratios with production modules

[Frightning]

So I like to use production modules everywhere I can, which leads me to having to determine the ratio of Electric Mining Drills to Electric Furnaces once Production Modules start being used (which will differ from the usual 160 miners to 147 furnaces ratio that happens without the modules). This is a fair bit more complex than the no module case due to the fact that production modules boost yield, but slow speed. These ratios also change depending on the levels of the modules used, so for simplicity, I will assume all the same level:

Iron and Copper ratios:
Production Module 1s:
Electric Miner ore mining speed: 0.525/s*(1-0.15*3)=0.525*0.55/s=0.28875/s
Electric Miner ore yield: 0.28875/s*(1+0.04*3)=0.28875*1.12/s=0.3234/s
Electric Furnace ore consumption rate: 0.(571428)/s*(1-0.15*2)=0.(571428)*0.7/s=0.4/s
Electric Furnace plate production speed: 0.4/s*(1+0.04*2)=0.4*1.08/s=0.432/s
Miner to Furnace ratio: 0.4 miners to 0.3234 furnaces=2000 miners to 1617 furnaces
(roughly 5 miners to 4 furnaces)

Production Module 2s:
Electric Miner ore mining speed: 0.525/s*(1-0.15*3)=0.525*0.55/s=0.28875/s
Electric Miner ore yield: 0.28875/s*(1+0.06*3)=0.28875*1.18/s=0.340725/s
Electric Furnace ore consumption rate: 0.(571428)/s*(1-0.15*2)=0.(571428)*0.7/s=0.4/s
Electric Furnace plate production speed: 0.4/s*(1+0.06*2)=0.4*1.12/s=0.448/s
Miner to Furnace ratio: 0.4 miners to 0.340725 furnaces=16000 miners to 13629 furnaces
(roughly 20 miners to 17 furnaces)

Production Module 3s:
Electric Miner ore mining speed: 0.525/s*(1-0.15*3)=0.525*0.55/s=0.28875/s
Electric Miner ore yield: 0.28875/s*(1+0.1*3)=0.28875*1.3/s=0.375375/s
Electric Furnace ore consumption rate: 0.(571428)/s*(1-0.15*2)=0.(571428)*0.7/s=0.4/s
Electric Furnace plate production speed: 0.4/s*(1+0.1*2)=0.4*1.2/s=0.48/s
Miner to Furnace ratio: 0.4 miners to 0.340725 furnaces=3200 miners to 3003 furnaces
(roughly 16 miners to 15 furnaces)

Stone ratios:
Production Module 1s:
Electric Miner stone mining speed: 0.65/s*(1-0.15*3)=0.65*0.55/s=0.3575/s
Electric Miner stone yield: 0.3575/s*(1+0.04*3)=0.3575*1.12/s=0.4004/s
Electric Furnace stone consumption rate: 1.(142857)/s*(1-0.15*2)=1.(142857)*0.7/s=0.8/s
Electric Furnace brick production speed: 0.4/s*(1+0.04*2)=0.4*1.08/s=0.432/s
Miner to Furnace ratio: 0.8 miners to 0.4004 furnaces=2000 miners to 1001 furnaces
(roughly 2 miners to 1 furnace)

Production Module 2s:
Electric Miner stone mining speed: 0.65/s*(1-0.15*3)=0.65*0.55/s=0.3575/s
Electric Miner stone yield: 0.3575/s*(1+0.06*3)=0.3575*1.18/s=0.42185/s
Electric Furnace stone consumption rate: 1.(142857)/s*(1-0.15*2)=1.(142857)*0.7/s=0.8/s
Electric Furnace brick production speed: 0.4/s*(1+0.06*2)=0.4*1.12/s=0.448/s
Miner to Furnace ratio: 0.8 miners to 0.42185 furnaces=16000 miners to 8437 furnaces
(roughly 40 miners to 21 furnaces)

Production Module 3s:
Electric Miner ore mining speed: 0.65/s*(1-0.15*3)=0.65*0.55/s=0.3575/s
Electric Miner ore yield: 0.3575/s*(1+0.1*3)=0.3575*1.3/s=0.46475/s
Electric Furnace ore consumption rate: 1.(142857)/s*(1-0.15*2)=1.(142857)*0.7/s=0.8/s
Electric Furnace brick production speed: 0.4/s*(1+0.1*2)=0.4*1.2/s=0.48/s
Miner to Furnace ratio: 0.8 miners to 0.46475 furnaces=3200 miners to 1859 furnaces
(roughly 160 miners to 93 furnaces)

Steel Ratios:
Production Module 1s:
Electric Furnace iron ore consumption: 0.(571428)/s*(1-0.15*2)=0.(571428)*0.7/s=0.4/s
Electric Furnace iron ore yield: 0.4/s*(1+0.04*2)=0.4*1.08/s=0.432/s
Electric Furnace iron plate consumption rate: 0.(571428)/s*(1-0.15*2)=0.(571428)*0.7/s=0.4/s
Electric Furnace steel plate production speed: 0.1(142857)/s*(1+0.04*2)=0.1(142857)*1.08/s=0.123(428571)/s
Furnace (steel) to Furnace (iron) ratio: 0.432 steel to 0.4 iron=27 steel to 25 iron

Production Module 2s:
Electric Furnace iron ore consumption: 0.(571428)/s*(1-0.15*2)=0.(571428)*0.7/s=0.4/s
Electric Furnace iron ore yield: 0.4/s*(1+0.06*2)=0.4*1.12/s=0.448/s
Electric Furnace iron plate consumption rate: 0.(571428)/s*(1-0.15*2)=0.(571428)*0.7/s=0.4/s
Electric Furnace steel plate production speed: 0.1(142857)/s*(1+0.06*2)=0.1(142857)*1.12/s=0.128/s
Furnace (steel) to Furnace (iron) ratio: 0.448 steel to 0.4 iron=28 steel to 25 iron

Production Module 3s:
Electric Furnace iron ore consumption: 0.(571428)/s*(1-0.15*2)=0.(571428)*0.7/s=0.4/s
Electric Furnace iron ore yield: 0.4/s*(1+0.1*2)=0.4*1.2/s=0.48/s
Electric Furnace iron plate consumption rate: 0.(571428)/s*(1-0.15*2)=0.(571428)*0.7/s=0.4/s
Electric Furnace steel plate production speed: 0.1(142857)/s*(1+0.1*2)=0.1(142857)*1.2/s=0.13(714285)/s
Furnace (steel) to Furnace (iron) ratio: 0.48 steel to 0.4 iron=6 steel to 5 iron