1. Balancing Feed Rations Mathematical Applications in Agriculture, Food, and Natural Resources 130.10 (c) 3 B

2. One Minute! Write down everything you ate yesterday

4. 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

5. 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

6. 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

7. 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?

8. 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

9. 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

10. Step 3: Subtract 12% CP Corn 8.9% CP SBM 44.4% CP _____ parts Corn _____ parts SBM Subtract diagonally: 44.4 – 12 = 32.4 32.4

11. 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 3.1 32.4 3.1

12. Step 4: Add 12% CP Corn 8.9% CP SBM 44.4% CP _____ parts Corn _____ parts SBM Add parts of each feed: 32.4 + 3.1 = 35.5 32.4 3.1 35.5 Total Parts

13. 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

14. 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 = 639.1 lbs. of Corn SBM: 700 lbs. x.087 = 60.9 lbs. of SBM

15. Step 7: Check Your Work Add up the feedstuff totals to be sure they equal the total ration amount. 639.1 lbs. of Corn + 60.9 lbs. of SBM = 700 lbs. of feed

16. Step 7: Check Your Work Corn (8.9% CP): 639.1 lbs. 639.1 lbs. x.089 CP = 56.9 lbs. CP SBM (44.4% CP): 60.9 lbs. 60.9 lbs. x.444 CP = 27.0 lbs. CP Add for total lbs. CP 56.9 lbs. CP + 27.0 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

17. Answer Marvin needs 639.1 lbs. of Corn and 60.9 lbs. of SBM to make 700 lbs. of feed for his sows

18. 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

19. 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?

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

21. 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

22. Practice Alfalfa: 7.6 / 12.7 =.598 x 100 = 59.8% Alfalfa – 300 lbs. x.598 = 179.4 lbs. Alfalfa Clover: 5.1 / 12.7 =.402 x 100 = 40.2% Clover – 300 lbs. x.402 = 120.6 lbs. Clover Check your work – 179.4 lbs. Alfalfa x.171 CP = 30.68 lbs. CP – 120.6 lbs. Clover x.044 CP = 5.31 lbs. CP – 30.68 lbs. CP + 5.31 lbs. CP = 35.99 lbs. CP – 35.99 lbs. CP / 300 lbs. = 12.00% CP

23. Answer Angela needs 179.4 lbs. of Alfalfa hay and 120.6 lbs. Clover to make 300 lbs. of feed for her rabbits.

24. Independent Practice Complete “Pearson Square” Worksheet