Balancing Feed Rations Mathematical Applications in Agriculture, Food, and Natural Resources (c) 3 B

One Minute! Write down everything you ate yesterday

Ration A ration is the total amount of feed consumed in a 24 hour period A ration should provide the proper proportion of each nutrient specific to the animal’s needs

Steps to Developing a Ration 1.Identify needs of the animal 2.Identify available feedstuffs 3.Calculate the amount of each feedstuff to use in the ration 4.Check the ration against nutrient needs

Pearson Square Method used to balance the nutrient content of two feedstuffs in a ration Need to know: – Nutrient requirements of animal – Nutrient content of feedstuff

Example Problem Marvin wants to formulate a feed ration that provides 12% Crude Protein (CP) for his sows. On hand he has corn which contains 8.9% CP and soybean meal which contains 44.4% CP. If Marvin wants 700 lbs. of feed, how much corn and soybean meal (SBM) should he use?

Step 1: Set up the Pearson Square Feed #1 Nutrient % Feed #2 Nutrient % Nutrient % Requirement of Animal Part of Feed #1 Needed Part of Feed #2 Needed

Step 2: Fill in the Square Feed #1 Nutrient % Feed #2 Nutrient % Nutrient % Requirement of Animal Parts of Feed #1 Needed Parts of Feed #2 Needed 12% CP Corn 8.9% CP SBM 44.4% CP _____ parts Corn _____ parts SBM

Step 3: Subtract 12% CP Corn 8.9% CP SBM 44.4% CP _____ parts Corn _____ parts SBM Subtract diagonally: 44.4 – 12 =

Step 3: Subtract 12% CP Corn 8.9% CP SBM 44.4% CP _____ parts Corn _____ parts SBM Subtract diagonally: 8.9 – 12 = -3.1 No negatives! Always use absolute value

Step 4: Add 12% CP Corn 8.9% CP SBM 44.4% CP _____ parts Corn _____ parts SBM Add parts of each feed: = Total Parts

Step 5: Convert Parts to % Formula: Parts / Whole x 100 = % Corn: 32.4 parts / 35.5 parts =.913 x 100 = 91.3% Corn SBM: 3.1 parts / 35.5 parts =.087 x 100 = 8.7% SBM

Step 6: Convert % to Lbs. Now we need to convert the % to lbs. to find out exactly how much of each ingredient will go into the ration. – We need 700 lbs. of feed for Marvin’s sows Total lbs. of ration x decimal form of feed % = Total lbs. of feedstuff Corn: 700 lbs. x.913 = lbs. of Corn SBM: 700 lbs. x.087 = 60.9 lbs. of SBM

Step 7: Check Your Work Add up the feedstuff totals to be sure they equal the total ration amount lbs. of Corn lbs. of SBM = 700 lbs. of feed

Step 7: Check Your Work Corn (8.9% CP): lbs lbs. x.089 CP = 56.9 lbs. CP SBM (44.4% CP): 60.9 lbs lbs. x.444 CP = 27.0 lbs. CP Add for total lbs. CP 56.9 lbs. CP lbs. CP = 83.9 lbs. CP Divide by total feed for nutrient requirement (83.9 lbs. CP / 700 lbs.) x 100 = 12% CP for Sows

Answer Marvin needs lbs. of Corn and 60.9 lbs. of SBM to make 700 lbs. of feed for his sows

Algebraically.12 CP x 700 lbs. = 84 lbs. of CP required in Marvin’s sow feed.089x +.444y = 84 lbs. CP x + y = 700 lb. feed X = 639.1, Y = 60.9

Practice Angela needs 300 lbs. of rabbit feed containing 12% CP. She wants to formulate a ration containing alfalfa hay at 17.1% CP and clover at 4.4% CP. How much clover and alfalfa hay should Angela use to make her feed?

Practice Feed #1 Nutrient % Feed #2 Nutrient % Nutrient % Requirement of Animal Part of Feed #1 Needed Part of Feed #2 Needed

Practice Feed #1 Nutrient % Feed #2 Nutrient % Nutrient % Requirement of Animal Parts of Feed #1 Needed Parts of Feed #2 Needed 12% CP Alfalfa 17.1% CP Clover 4.4% CP 7.6 parts Alfalfa 5.1 parts Clover 12.7 Total Parts

Practice Alfalfa: 7.6 / 12.7 =.598 x 100 = 59.8% Alfalfa – 300 lbs. x.598 = lbs. Alfalfa Clover: 5.1 / 12.7 =.402 x 100 = 40.2% Clover – 300 lbs. x.402 = lbs. Clover Check your work – lbs. Alfalfa x.171 CP = lbs. CP – lbs. Clover x.044 CP = 5.31 lbs. CP – lbs. CP lbs. CP = lbs. CP – lbs. CP / 300 lbs. = 12.00% CP

Answer Angela needs lbs. of Alfalfa hay and lbs. Clover to make 300 lbs. of feed for her rabbits.

Independent Practice Complete “Pearson Square” Worksheet