Balancing Rations
A)  Formulate a swine diet containing 20% CP using corn and soybean meal.  As-fed basis.

1)  From packet:  Corn = 8.8% CP
SBM = 45.7% CP

2)  X = % corn
     100 - X = % SBM

3)   .088(X) + .457(100 - X) = 20
    .088(X) + 45.7 - .457(X) = 20
    -.369(X) = 20 - 45.7
  X = 69.65

4)  Final Diet
69.65%  Corn
30.35%  SBM

B)  Prepare 1 ton of a swine diet containing 16% CP from corn and a mixture of SBM and meat tankage (3 parts SBM to 1 part tankage).  As-fed basis.

1)  From Packet:  Corn = 8.8% CP
SBM = 45.7% CP
Tankage = 47.2% CP

2)  Determine CP content of SBM/tankage mix.
3(45.7) + 1(47.2)  = 46.075% CP in mix
          4

3)  X = lbs Corn
     2000 - X = lbs Mix

4)  .088(X) + .46075(2000 - X) = 320
   X = 1613.68

5)  Final Diet
1613.68 lbs Corn
 289.74 lbs SBM
   96.58 lbs meat meal tankage

C)  Fixed Ingredients:  Formulate 1 ton of a cattle diet that contains 12.5% CP.  The diet will contain 17% oats and 3% of a vitamin/mineral premix as fixed ingredients.  Remainder of the diet will be corn and cottonseed meal.  As-fed basis.

1)  Amount of fixed ingredient and CP from each.
2000 X .17 = 340 lbs oats   X .091 = 30.94 lb CP
2000 X .03 =  60 lbs v/m pmx X 0 = 0 lb CP     
                                         400 lbs                     30.94 lbs CP

2)  Need 250 lbs CP
 - 30.94
            219.06 lbs CP still needed from corn and CSM

3)  X = lbs Corn
     1600 - X = lbs CSM

4)  .088(X) + .443(1600 - X) = 219.06
       -.355X = -489.74
              X = 1379.55

5)  Final Diet
         1379.55 lbs Corn
           220.45 lbs CSM
  340 lbs Oats
   60 lbs Vit/Min Premix