Algebraic method

ALGEBRAIC METHOD
  • Divide the ingredients into two groups ie. Low protein group and high protein group depending on their protein content.
  • Calculate the average protein content of each group, if there is more than one feed ingredient.
  • Assume that ‘X’ represents the amount of low protein feeds and ‘Y’ represents the amount of high protein feeds present in 100 kg of concentrate mixture. That means,

X + Y = 100 ---------- (1)

Note:

X + Y = 97 -----------(1)

  • For example, assume that

Average CP/DCP content of low protein group is 8 %

This means, 100 kg of feed will contain 8 kg CP/DCP

Therefore, the amount of CP/DCP supplied through ‘X’ kg will be

= X * 8 / 100 = 0.08 X kg.50

b. Average CP/DCP content of high protein group is 40 %

This means, 100 kg of feed will contain 40 kg CP/DCP

Therefore, the amount of CP/DCP supplied through ‘Y’ kg will be

= Y * 40 / 100 = 0.40Y kg.

c. However, the amount of CP/DCP being supplied through low and high protein feeds should be equal to the desired protein level (say 18%). So,

0.08 X + 0.40 Y = 18 --------------- (2)

  • Calculate the value of ‘X’ and ‘Y’ from the above two equations.
  • Now, ‘X’ and ‘Y’ representing the amount of low and high protein feeds should be divided equally, depending on the number of ingredients in each group.
  • Check whether the calculated proportion of each ingredient when mixed together is supplying the desired CP/DCP content or not.

In case, the amount of mineral mixture and salt to be included in the ration are fixed say 2 and 1% respectively, then this fixed proportion of 3% should be subtracted from the total quantity of conc. Mixture. In such case

Example

  • Prepare 100 kg concentrate mixture containing 18 % DCP using maize grain, wheat bran and linseed cake consisting of 10, 12 and 30 % DCP respectively.

Solution

Let

Average DCP content of low protein group = 10 + 12 / 2 = 11 %

Average DCP content of high protein group = 30 %

Assume that ‘X’ represents the amount of low protein feeds and ‘Y’ represents the amount of high protein feeds present in 100 kg of concentrate mixture. That means,

X + Y = 100 ---------- (1)

Average DCP content of low protein group is 11 %

This means, 100 kg of feed will contain 11 kg DCP

Therefore, the amount of DCP supplied through ‘X’ kg will be

= X * 11 / 100 = 0.11X.51

Average DCP content of high protein group is 30%

This means, 100 kg of feed will contain 30 kg DCP

Therefore, the amount of DCP supplied through ‘Y’ kg will be

= Y * 30 / 100 = 0.30Y.

c. However, the amount of DCP being supplied through low and high protein feeds should be equal to the desired protein level (say 18 %).

So,

0.11X + 0.30Y = 18 ---------------(2)

Multiplying equation (1) by 0.3 we get

0.3X + 0.3Y = 30 ----------(3)

Subtracting equation (3) from (2)

0.11X + 0.30Y = 18---------------(2)

0.3X + 0.3Y = 30 --------------(3)

0.19X = 12

or X = 12 / 0.19 = 63.16 or 63 parts

and Y = 100 – 63 = 37 parts.

Therefore,

No. of parts of maize = 63 / 2 = 31.5

No. of parts of wheat bran = 63 – 31.5 = 31.5

No. of parts of linseed cake = 37

Verification

  • Maize and wheat bran represent low protein group and linseed cake represent high protein group.
Feedstuff
Parts
% DCP supplied
Linseed cake
37.0
37 x 30 /100 = 11.10
Maize
31.5
31.5 x 10 /100 = 3.15
Wheat bran
31.5
31.5 x 12 / 100 = 3.78
Total
100
18.03
Last modified: Tuesday, 3 April 2012, 10:00 AM