I dont get why you take 70 % of 130 000 lbs ?
With your 4-2-8 rations i would have calculated corn used bases on lbs gained between Feeder and Live contratcts :
8*40000-4*50000 = 120 000 lbs. * FCR @ 6 = 720 000 / 56 lbs per bu. = 12857 bu ?
First: Your calculation of the total lbs of 8 Live cattle = 320,000 less the total lbs. of 4 Feeders = 200,000 to get the total weight gain of 120,000 lbs is correct.
My calculation as stated is based on 500 lbs gain per Head. 1 feeder = 50,000 / 750 = 66.66666666666+ head. 2 Live @ 40,000 = 80,000 / 1250 lbs = 64 head. So I took an average of 65 head per spread.
4 x 65 = 260 head, x 500 = 130,000 lbs of weight gain. So the deference of 120,000 vs. 130,000 is due to the way I rounded, 320,000 / 1250 lbs only = 256 head. 200,000 / 750 = 266.66666666666+ head. (a little more then 10 head per)
Next: You have the 120,000 lbs gain x 6 to get 720,000 lbs / 56 lbs per bu. to get the 12,857 bu. That's correct
@ 100% corn rations. However @ 70% you get 84,000 lbs. gain x FCR 6 = 504,000 / 56 lbs. per bu. to get 9,000 bu. At 75% one gets 90,000 lbs. gain x 6 = 540,000 / 56 lbs per bu. = 9,643 bu.
If one looks at the Feed Rations, I've seen it as low as 5.13% and as high as 86% of No. 2 Corn. On the high end, No. 2 is all the corn given with 22% alfalfa + 2% protein supplement. On the low end another 51% feed from Corn Silage* and 41% alfalfa + about 2.5 in supplements. The feed rations will vary from Steers and Heifers, season and age of the calf to get the best FCR & Daily Weight possible if the feedlot operator is running an efficient operation. Note: In the recent past I've seen the total corn ration drop to as low as 40 to 45% during the drought. This was due not so much to the high price but to availability in some regions. The beef industry is in constant change, the operations of producer, cattle finishing, and final processing are becoming more and more integrated, further improvements in the FCR and increased use of distillers grains may change the spread yet again.
*Corn silage for (lower grade corn) beef rations that produce 1-1/4 to 2 pounds daily growth gain. It works well for starting cattle on feed from range feed. Cattle are easily changed from corn silage to a high-grain finishing ration. Corn silage is often used to furnish minimum roughage levels in high-grain finishing rations.