Week 6

Ration Formulation

Pearson's Square and Double Pearson's Square Examples

Text Transcript

Pearson's Square Example

Formulate a finishing diet containing 80% TDN on a DM basis. The feeds to be used are roughage (60% TDN on a DM basis) and a concentrate mix containing 83% TDN on a DM basis.

Place the percent TDN (you can balance for any nutrient usin gthis method) desired in the combination of the two feeds in the center of a square and the percent TDN content of each feed at the left corners as shown in the figure below.

Subtract diagonally across the square, the smaller number from the larger without regard for the sign and record the difference at the right corners.

The parts of each feed can be expressed as a % of the total.

Precaution about using the Pearson Square. The number in the center of the square must be intermediate (i.e. in between) to the two numbers at the left corners. If not, then the ration cannot be balanced.

Roughage and the concentrate contain 35 and 91% DM, respectively.

What is the ingredient composition of the diet on an as-fed basis?

Roughage costs $35 per ton and the concentrate costs $180/ton.

How much does the diet cost per ton AF?

Suppose the steers in this example are consuming 25.0 lbs. (AF basis) of your mix per day. What is the feed cost per animal per day?

$1.29 =25/2000*$103.35

The steers are gaining 3.5 lbs. per day. Calculate feed efficiency (lbs. feed/lbs. gain) and calculate cost per pound of gain.

=25 AF lbs x 28.1% roughage = 7.0 AF lbs x 35% DM = 2.5 lbs DM
=25 AF lbs x 71.9% concentrate = 18.0 AF lbs x 91% DM = 16.4 lbs DM
Total of 18.9 lbs DM

Feed Efficiency = 5.4 =18.9 lbs DM/3.5 lbs gain
Cost per pound of gain = $ 0.37 =1.29/3.5

Double Pearson's Square Example

Suppose we want a final mix with 16% CP and 72% TDN. We have corn silage with 9% and 68%, concentrate with 24% and 79%, and alfalfa hay with 20% and 68% CP and TDN, respectively.

The ration would contain 77.9% Mix 1 and 22.1% Mix 2. Corn Silage was in both squares or mixes, so there are two calculations needed to dtermine the total amount of corn silage and only one calculation each to determine the amounts of Concentrate and Alfalfa Hay. Calculations for individual ingredients are shown in the table below.

Precaution about using the Double Pearson Square. The number in the center of the square must be intermediate (i.e. in between) to the two numbers at the left corners, which was CP in the example. In addition, the goal TDN must be intermediate to the TDN of the two mixes. If not, then the ration cannot be balanced.

Corn, CSM, and Alfalfa contain 30, 91, and 88% DM, respectively. What is the ingredient composition of the diet on an as-fed basis?

Corn costs $35 per ton, concentrate costs $200/ton, and Alfalfa costs $65/ton. How much does the diet cost per ton AF?

Suppose the cows in this example are consuming 110.0 lbs. (AF basis) of your mix per day. What is the feed cost per animal per day?

$4.07 =110/2000*$80.97

How many lbs of DM are the cows consuming?

Suppose the cows in this example are producing 75 lbs milk. What is the feed cost per cwt milk?

$5.42 =100/75*$4.07