Feed formulation worksheet with protein content data for ingredients like corn, soybean meal, fishmeal, and poultry feeds.

Let’s solve each problem step by step using the Pearson Square method (also called the alligation method), which is perfect for blending two ingredients to get a desired protein percentage.

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Problem 1:

Using corn (8.8% CP) and soybean meal (44.0% CP), blend to make an 18% CP ration. How many lbs of each to make 1000 lbs?

Step 1: Set up Pearson Square

```
Corn (8.8%) | 44.0 - 18.0 = 26.0 parts
|
Desired (18.0%) |
|
Soybean (44.0%) | 18.0 - 8.8 = 9.2 parts
```

Total parts = 26.0 + 9.2 = 35.2 parts

Step 2: Find weight per part
Total mixture = 1000 lbs
So, 1 part = 1000 ÷ 35.2 ≈ 28.409 lbs

Step 3: Calculate each ingredient
- Corn = 26.0 parts × 28.409 ≈ 738.6 lbs
- Soybean meal = 9.2 parts × 28.409 ≈ 261.4 lbs

Check: 738.6 + 261.4 = 1000 lbs ✔
Protein check:
(738.6 × 8.8 + 261.4 × 44.0) / 1000 =
(6499.68 + 11501.6) / 1000 = 18001.28 / 1000 ≈ 18.0% ✔

✔ Final Answer for #1:
Corn: 738.6 lbs, Soybean meal: 261.4 lbs

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Problem 2:

Using finisher feed (14% CP) and soybean meal (44.0% CP), blend to make 18% CP ration. Make 2000 lbs total.

Pearson Square:

```
Finisher (14%) | 44.0 - 18.0 = 26.0 parts
|
Desired (18.0%) |
|
Soybean (44.0%) | 18.0 - 14.0 = 4.0 parts
```

Total parts = 26.0 + 4.0 = 30.0 parts

Weight per part = 2000 ÷ 30.0 ≈ 66.667 lbs

- Finisher = 26.0 × 66.667 ≈ 1733.3 lbs
- Soybean meal = 4.0 × 66.667 ≈ 266.7 lbs

Check: 1733.3 + 266.7 = 2000 lbs ✔
Protein: (1733.3×14 + 266.7×44)/2000 =
(24266.2 + 11734.8)/2000 = 36001/2000 ≈ 18.0% ✔

✔ Final Answer for #2:
Finisher feed: 1733.3 lbs, Soybean meal: 266.7 lbs

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Problem 3:

Formulate 1 ton (2000 lbs) of pig starter with 18% CP using corn (9% CP) and soybean meal (44% CP).

Note: The table says corn is 8.8%, but question says “corn (9% CP)” — we’ll use 9% as given in the question.

Pearson Square:

```
Corn (9%) | 44 - 18 = 26 parts
|
Desired (18%) |
|
Soybean (44%) | 18 - 9 = 9 parts
```

Total parts = 26 + 9 = 35 parts

Weight per part = 2000 ÷ 35 ≈ 57.143 lbs

- Corn = 26 × 57.143 ≈ 1485.7 lbs
- Soybean meal = 9 × 57.143 ≈ 514.3 lbs

Check: 1485.7 + 514.3 = 2000 lbs ✔
Protein: (1485.7×9 + 514.3×44)/2000 =
(13371.3 + 22629.2)/2000 = 36000.5/2000 ≈ 18.0% ✔

✔ Final Answer for #3:
Corn: 1485.7 lbs, Soybean meal: 514.3 lbs

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Problem 4:

Formulate 2 tons (4000 lbs) of fish diet with 32% CP using corn (9% CP) and fish meal (48% CP).

Note: Table says fishmeal is 53.6%, but question says “fish meal (48% CP)” — we’ll use 48% as given.

Pearson Square:

```
Corn (9%) | 48 - 32 = 16 parts
|
Desired (32%) |
|
Fish meal (48%) | 32 - 9 = 23 parts
```

Total parts = 16 + 23 = 39 parts

Weight per part = 4000 ÷ 39 ≈ 102.564 lbs

- Corn = 16 × 102.564 ≈ 1641.0 lbs
- Fish meal = 23 × 102.564 ≈ 2359.0 lbs

Check: 1641.0 + 2359.0 = 4000 lbs ✔
Protein: (1641×9 + 2359×48)/4000 =
(14769 + 113232)/4000 = 128001/4000 ≈ 32.0% ✔

✔ Final Answer for #4:
Corn: 1641.0 lbs, Fish meal: 2359.0 lbs

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Final Answer:
1) Corn: 738.6 lbs, Soybean meal: 261.4 lbs
2) Finisher feed: 1733.3 lbs, Soybean meal: 266.7 lbs
3) Corn: 1485.7 lbs, Soybean meal: 514.3 lbs
4) Corn: 1641.0 lbs, Fish meal: 2359.0 lbs