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Matrix Technique in Ration Formulation
750
RESEARCH NOTES
MATRIX TECHNIQUE IN RATION FORMULATION T. SELVARAJAH, J. D. SUMMERS AND F. N. JEROME Department of Poultry Science, University of Guelph, Guelph, Ontario, Canada (Received for publication March 11, 1969)
PC" 1 = A where, P is a l X n row vector with the elements representing the desired M.E. expressed in Kcal./lb.
and nutrients can be formulated accurately in a very short time. The following is an example of a ration made up of three ingredients, namely, ground yellow corn, soybean meal (50% protein) and animal fat (stabilised). In this case, it is desired to formulate a ration which will give the following values: M. E. = 1350 Kcal./lb., Crude Protein = 17% and Crude Fat = 4% The above values are then listed as the elements of the row vector P, and the composition of the different ingredients are listed as the elements of the matrix C, as explained earlier. Thus,
100 and the desired percentages of the different nutrients; C is an nXn matrix of values which indicate the composition of the feed ingredients employed in the ration, the columns representing the energy
M.E.
and different nutrient percentages, and the rows representing the different ingredients employed in the ration; (C - 1 is the inverse of matrix C); and A, the resulting l X n row vector, gives the proportions of the different ingredients that should be mixed to obtain a ration with the desired M.E. and percentages of other nutrients. The advantage of the technique is that once a table of inverted matrices for different combinations of ingredients is available, the matrix multiplication can be very simply performed and any number of rations with different levels of M.E.
% Fat
17.0
4.0]
P = [13.50 and "14.8
8.6
C = 11.2
50.0
.34.8
(Kcal./lb.) 100
% Protein
0
3.6~|corn 0.5 soy 100.0. fat
Matrix C is then inverted (and this can easily be done with the assistance of a computer) to give: ' 1
C" =
0.0863 -0.0149 -0.0032
-0.0190
0.0233
0.0006
.-0.0300
0.0052
0.0111
Multiplying the vector P by the inverted matrix C _1 will then give the vector A, where the elements will represent the proportions of the different ingredients that should be mixed to obtain the desired levels of M.E., crude protein and crude fat. The multiplication is accomplished as follows:
Downloaded from http://ps.oxfordjournals.org/ at Karolinska Institutet University Library on May 31, 2015
A simple technique utilising matrix algebra has been developed for the quick and efficient formulation of rations with desired levels of energy and other nutrients. The technique involves matrix inversion and multiplication and can be represented as follows:
751
RESEARCH NOTES
c-1
P 17.0
13.50
= (13.50X
0.0863)
4.0]
X
0.0863
-0.0149
-0.0032
0.0190
0.0233
0.0006
0.0300
0.0052
0.0111
(13.50X-0.0149)
(13.50X-0.0032)
+ (17.0 X0.0233)
+ (17.OX
0.0006)
+ (4.0 X - 0 . 0 3 0 0 )
+ (4.0 X
+ (4.0 +
0.0111)
[(0.7220) Corn
0.0052)
(0.2158)
(0.0114)] = A
Soy
Fat
Thus, the proportions of corn, soybean meal, and stabilised fat that must be mixed to give the desired ration are 72.2% corn, 21.58% soybean meal and 1.14% stabilised fat, and the remaining 5.08% (to make up the 100%) would be made up of vitamin/mineral premix and some inert ingredient such as alpha floe. This percentage would normally vary from 0 to 5%, depending on the ration desired and
ingredients used. Note: I t should be noted that every set of ingredients has limitations with respect to the desired levels of energy and nutrients in the resulting ration. Hence, if a solution is not possible by the method described above, it would indicate that the desired levels of energy and nutrients are beyond the scope of the ingredients used.
HATCHABILITY OF CHICKEN EMBRYOS UNDER SIMULATED HIGH ALTITUDE CONDITIONS* R. P. TENGERDY, J. W. FITCH AND R. E. MORENG Departments of Microbiology, Physiology, and Avian Science, Colorado State University, Fort Collins, Colorado 80521 (Received for publication March 13, 1969)
High altitude decreases the hatchability of chicken eggs and has some cellular and physiologic effects on young and adult chickens. Francis et al. (1967) observed that the hatchability of eggs from the same strain decreased 10 percent at a 305 m. increase in altitude, 20 percent at a 610 m. in* Partially supported by NASA-SUP Grant 1914.
crease. These authors also reviewed the earlier literature of altitude effects on hatchability. A significant reduction in hatchability was also reported by Stephens and Ploog (1967), working at a natural altitude of 3,200 m. in Peru. However, Fraps (1945) did not record any significant reduction in the ability of the embryo to hatch until the pressure was reduced to 12.5 mm. of Hg (27,000 m.) for a
Downloaded from http://ps.oxfordjournals.org/ at Karolinska Institutet University Library on May 31, 2015
+ (17.0 X - 0 . 0 1 9 0 )
RESEARCH NOTES
MATRIX TECHNIQUE IN RATION FORMULATION T. SELVARAJAH, J. D. SUMMERS AND F. N. JEROME Department of Poultry Science, University of Guelph, Guelph, Ontario, Canada (Received for publication March 11, 1969)
PC" 1 = A where, P is a l X n row vector with the elements representing the desired M.E. expressed in Kcal./lb.
and nutrients can be formulated accurately in a very short time. The following is an example of a ration made up of three ingredients, namely, ground yellow corn, soybean meal (50% protein) and animal fat (stabilised). In this case, it is desired to formulate a ration which will give the following values: M. E. = 1350 Kcal./lb., Crude Protein = 17% and Crude Fat = 4% The above values are then listed as the elements of the row vector P, and the composition of the different ingredients are listed as the elements of the matrix C, as explained earlier. Thus,
100 and the desired percentages of the different nutrients; C is an nXn matrix of values which indicate the composition of the feed ingredients employed in the ration, the columns representing the energy
M.E.
and different nutrient percentages, and the rows representing the different ingredients employed in the ration; (C - 1 is the inverse of matrix C); and A, the resulting l X n row vector, gives the proportions of the different ingredients that should be mixed to obtain a ration with the desired M.E. and percentages of other nutrients. The advantage of the technique is that once a table of inverted matrices for different combinations of ingredients is available, the matrix multiplication can be very simply performed and any number of rations with different levels of M.E.
% Fat
17.0
4.0]
P = [13.50 and "14.8
8.6
C = 11.2
50.0
.34.8
(Kcal./lb.) 100
% Protein
0
3.6~|corn 0.5 soy 100.0. fat
Matrix C is then inverted (and this can easily be done with the assistance of a computer) to give: ' 1
C" =
0.0863 -0.0149 -0.0032
-0.0190
0.0233
0.0006
.-0.0300
0.0052
0.0111
Multiplying the vector P by the inverted matrix C _1 will then give the vector A, where the elements will represent the proportions of the different ingredients that should be mixed to obtain the desired levels of M.E., crude protein and crude fat. The multiplication is accomplished as follows:
Downloaded from http://ps.oxfordjournals.org/ at Karolinska Institutet University Library on May 31, 2015
A simple technique utilising matrix algebra has been developed for the quick and efficient formulation of rations with desired levels of energy and other nutrients. The technique involves matrix inversion and multiplication and can be represented as follows:
751
RESEARCH NOTES
c-1
P 17.0
13.50
= (13.50X
0.0863)
4.0]
X
0.0863
-0.0149
-0.0032
0.0190
0.0233
0.0006
0.0300
0.0052
0.0111
(13.50X-0.0149)
(13.50X-0.0032)
+ (17.0 X0.0233)
+ (17.OX
0.0006)
+ (4.0 X - 0 . 0 3 0 0 )
+ (4.0 X
+ (4.0 +
0.0111)
[(0.7220) Corn
0.0052)
(0.2158)
(0.0114)] = A
Soy
Fat
Thus, the proportions of corn, soybean meal, and stabilised fat that must be mixed to give the desired ration are 72.2% corn, 21.58% soybean meal and 1.14% stabilised fat, and the remaining 5.08% (to make up the 100%) would be made up of vitamin/mineral premix and some inert ingredient such as alpha floe. This percentage would normally vary from 0 to 5%, depending on the ration desired and
ingredients used. Note: I t should be noted that every set of ingredients has limitations with respect to the desired levels of energy and nutrients in the resulting ration. Hence, if a solution is not possible by the method described above, it would indicate that the desired levels of energy and nutrients are beyond the scope of the ingredients used.
HATCHABILITY OF CHICKEN EMBRYOS UNDER SIMULATED HIGH ALTITUDE CONDITIONS* R. P. TENGERDY, J. W. FITCH AND R. E. MORENG Departments of Microbiology, Physiology, and Avian Science, Colorado State University, Fort Collins, Colorado 80521 (Received for publication March 13, 1969)
High altitude decreases the hatchability of chicken eggs and has some cellular and physiologic effects on young and adult chickens. Francis et al. (1967) observed that the hatchability of eggs from the same strain decreased 10 percent at a 305 m. increase in altitude, 20 percent at a 610 m. in* Partially supported by NASA-SUP Grant 1914.
crease. These authors also reviewed the earlier literature of altitude effects on hatchability. A significant reduction in hatchability was also reported by Stephens and Ploog (1967), working at a natural altitude of 3,200 m. in Peru. However, Fraps (1945) did not record any significant reduction in the ability of the embryo to hatch until the pressure was reduced to 12.5 mm. of Hg (27,000 m.) for a
Downloaded from http://ps.oxfordjournals.org/ at Karolinska Institutet University Library on May 31, 2015
+ (17.0 X - 0 . 0 1 9 0 )