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Evaluating New or Improved Poultry Feedstuffs by Parametric Linear Programming Techniques
Evaluating New or Improved Poultry Feedstuffs by Parametric Linear Programming Techniques YVONNE DAVIES,1 W. K. TROTTER2 AND D. BURDICK1 U. S. Department of Agriculture (Received for publication April 5, 1972)
POULTRY SCIENCE 52:
INTRODUCTION
102-107,
1973
has another role not as widely known or EED represents the largest single cost used—the planning and economic evaluaitem in the production of poultry. Feed tion of research on new or improved feedaccounts for 62 percent of broiler produc- stuffs. This function is most successfully tion costs (Parkhurst, 1967). Minimizing performed by employing parametric linear feed costs through more efficient use of programming. Three parametric techavailable feedstuffs, therefore, is an impor- niques useful in research on feedstuffs are tant goal of all producers. In recent years described and illustrated in this paper. As a brief review, linear programming is the most effective means of attaining this goal has been the use of computers and lin- a mathematical procedure which solves a ear programming to formualte rations that series of linear equations simultaneously. meet the animal's nutritional requirements There are two essential steps in linear proat the lowest cost. This is now a widely ac- gramming. The first step is construction of cepted practice in the feed industry, with a mathematical model that represents the about 70 percent of the mixed feed in the problem to be solved. In ration formulation United States today being formulated by this involves setting up a matrix with rows computer (Enochian et al., 1971). Linear of constraints and columns of feed compoprogramming, by its rapid formulation of sition data. Diet requirements prescribe the economical and well-balanced rations, has constraints to be considered and include established its role as an important tool in both nutrient and nonnutrient elements. feed manufacturing. Linear programming Nutrient restrictions might be minimums and/ or maximums for protein, calcium, vi"Agricultural Research Service, Richard B. tamin A, metabolizable energy, etc. NonnuRussell Agricultural Research Center, Forage and trient restrictions might be pelletability or Feed Laboratory, Athens, Georgia 30604. palatability factors. The second step is so2 Economic Research Service, Richard B. Russell lution of the problem. This involves formuAgricultural Research Center, Liaison Group, lating that blend of ingredients which Athens, Georgia 30604.
F
102
Downloaded from http://ps.oxfordjournals.org/ by guest on May 7, 2015
ABSTRACT The use of linear programming and computers to formulate rations that meet the nutritional requirements of poultry at lowest cost is a widely accepted practice in the poultry feed industry. One application of linear programming not readily employed by poultry nutritionists is the use of parametric linear programming in the planning and economic evaluation of research on new or improved feedstuffs. Three parametric techniques useful in research are parametric cost ranging, parametric nutrient ranging, and parametric restriction ranging. Parametric cost ranging is useful in evaluating the market potential for new or improved feedstuffs and examining competitive and substitution relationships among ingredients. Parametric nutrient ranging, by analyzing at different levels the nutrient content of a particular feed ingredient, shows the changes in economic value that result from changes in the ingredient's nutrient composition. Parametric restriction ranging enables one to analyze the effect of changes in dietary requirements on ration cost and composition and to identify those nutrients for which diet requirements need to be more precisely denned.
LINEAR
PROGRAMMING EVALUATION OF FEEDS
PARAMETRIC COST RANGING Parametric cost ranging involves ranging the price of one or more ingredients while prices of other ingredients are held constant. Many ingredient prices can be ranged simultaneously, but the association of cause and effect is difficult when several cost factors are ranged. When an ingredient price is parameterized, P.C.R. shows the quantity of the traced feed ingredient which will be used in the least-cost ration at various price levels. This essentially gen-
Price ($/cwt)
0.50 K, ... Quantity in ration (Percent)
FIG. 1. Economic value curve for sunflower expeller meal in broiler finisher rations.
erates a steplike demand function for the traced ingredient (Figure 1). Such a curve gives the highest price at which the traced ingredient enters the ration and the increase in usage at successively lower prices. In this way, the economic value or nutritive worth of a particular feedstuff is quantified and an estimate of its potential market demand at different price levels can be made. The value will depend on the ingredient's nutrient composition and nutrient availability (if known), the composition and price of other ingredients, 3 diet requirements, and any bounds imposed on feed ingredients. When sunflower expeller meal 4 1 % was evaluated in broiler finisher rations, it had 'Feed ingredient prices used in this analysis were average prices for June 1971 and included all feedstuffs available on the Atlanta, Georgia, market.
Downloaded from http://ps.oxfordjournals.org/ by guest on May 7, 2015
meets diet requirements at the least cost. Selection among all available feedstuffs is based on the premise that feeds are interchangeable on a nutritional basis and is dependent upon complete and accurate composition data for all ingredients to be considered. Parametric linear programming is a refinement or sophistication of linear programming. Parametric programming traces the changes in the solution to a linear programming problem as one or more of the coefficients vary. I n this way flexibility is added to linear programming's rigid structure. The value of one or more coefficients in a row, column, or combination of row and column can be varied over a specified range. These coefficients can be prices of ingredients, nutrient content of ingredients, or diet requirements. Usually only one coefficient is parameterized (analyzed at different levels) while all other coefficients remain fixed. Whether the ranged coefficient is the cost of an ingredient, nutrient content of an ingredient, or diet restriction determines the name of the procedure. These are termed parametric cost ranging (P.C.R.), parametric nutrient ranging (P.N.R.), and parametric restriction ranging (P.R.R.), respectively. Each of these procedures will be discussed in terms of their role in the planning and economic evaluation of research on poultry feedstuffs.
103
104
Y. DAVIES, W. K. TROTTER AND D. BURDICK
Price ($/cwt)
15
20
25
Fie. 2. Economic value curves for sunflower expeller meal in three poultry diets.
a nutritive worth of $4.50 a hundredweight or $90 a ton. Results of the analysis are presented in Figure 1. At $90 a ton, sunflower meal forms 2 percent of the leastcost ration (Point A). This represents the first step of the discontinuous function. Sunflower meal increases to 6 percent of the ration if the price drops to $88 a ton (Point B). Further increases in usage occur at prices of $60, $58, and $14 a ton. However, since these are considerably below the selling price of $85 a ton, Points C, D, and E are of academic interest only. Parametric cost ranging is particularly useful when (1) developing a new ingredient or improving the quality of a known ingredient and an indication of its economic feasibility is required, (2) evaluating a new ingredient of known composition which has been introduced to the industry—as in the case of sunflower meal, (3) evaluating an ingredient in different rations or for feeding
TABLE 1.—A mino acid composition of sunfloiver meal 41%, soybean meal 44%, and egg protein Amino acid
Arginine Histidine Isoleucine Leucine Lysine Methionine Phenylalanine Threonine Tryptophan Valine
Sunflower meal 4 1 %
Soybean meal 44%
Egg protein
%
%
%
4.2 1.1 2.4 3.0 2.0 1.6 2.4 1.6 0.6 2.4
3.2 1.1 2.5 3.4 2.9 0.6 2.2 1.7 0.6 2.4
4.8 1.5 4.2 6.5 5.4 2.9 4.2 3.9 1.0 6.5
Downloaded from http://ps.oxfordjournals.org/ by guest on May 7, 2015
10
Quantity in ration (Percent)
to different species, (4) evaluating an ingredient on the basis of cost relationships at different market locations, and (5) evaluating competitive relationships among substitute ingredients. Another illustration of P.C.R.'s use in research is provided in Figure 2 where sunflower meal is evaluated for use in different poultry rations. In all three rations sunflower meal 4 1 % substitutes for soybean meal 44%. As shown in Table 1, lysine is sunflower's most limiting amino acid, but its high methionine content compared to soybean meal and other feed ingredients makes it valuable in poultry rations. Highest acceptance prices for the meal are $110, $90, and $86 a ton in the layer, broiler finisher, and broiler starter rations, respectively. Sunflower meal seems to have a greater potential as a protein supplement for layers than for broilers since at the market price it constitutes 13 percent of the least-cost layer ration, 6 percent of the broiler finisher ration, and 1 percent of the broiler starter ration. In these analyses, all input data were identical with the exception of diet requirements; therefore, any differences in valuation of the meal are due to differences in requirements. One factor that accounts for sunflower meal's superior showing in the layer diet is that layers, being more mature and having a greater di-
LINEAR PROGRAMMING EVALUATION OF FEEDS
gestive tract capacity than broilers, can accommodate more fiber in the ration; sunflower meal contains 13 percent crude fiber while soybean meal contains 7 percent fiber. Maximum limits on fiber in the poultry rations are 3.5 percent in the broiler starter diet, 4.0 percent in the broiler finisher diet, and 5.0 percent in the layer diet.
105
Increase in economic value ($/ton)
PARAMETRIC NUTRIENT RANGING
Increase in nutrient content (Percent)
FIG. 3. Relationship between improving the nutrient content of Coastal bermudagrass for broilers and increasing its economic value.
the improvement of Coastal's xanthophyll content would be more valuable dollarwise. Of course, any improvement in quality must be weighed against the added cost of processing to achieve this improved quality. PARAMETRIC RESTRICTION RANGING Parametric restriction ranging enables one to analyze at different levels the dietary requirement for a particular nutrient or nonnutrient. One or more requirements can be ranged simultaneously, but it is most beneficial to analyze a single requirement. P.R.R. shows the changes in ration cost and composition that occur when a given diet requirement is relaxed or tightened. From an examination of the cost of each diet restriction and the critical points at which these costs change, the nutritionist can identify those areas most in need of nutrition research. In this sense, P.R.R. can serve as a guide to determine where research priorities should be placed. Research should be conducted to narrow the safety margins on the costly diet restrictions, whereas research effort need not be expended on precisely defining requirements
Downloaded from http://ps.oxfordjournals.org/ by guest on May 7, 2015
Parametric nutrient ranging involves analyzing at different levels the nutrient content of a particular feed ingredient. P.N.R. shows the changes in economic value that the ingredient undergoes when its nutrient composition is improved or enhanced. Nutrients are assigned importance on the basis of their cost. Research efforts too should be directed to those areas where the greatest economic gain can be realized. Parametric nutrient ranging can help identify and establish priorities for the research needed to improve the nutritional value of feedstuffs. Parametrics can be of use in evaluating alternative research projects, especially in deciding on the best course of action when contemplating improvement in the nutrient content of an ingredient. The nutrient composition and nutrient availability of ingredients can be altered in many ways—by processing procedures, chemical or enzymatic modification, fermentation, storage and handling practices, time-of-harvest, or plant breeding. Using P.N.R. we can determine what alterations would be most beneficial in terms of cost and then initiate research to provide specific nutrients at a predetermined level. Results of a P.N.R. study indicate that a 10 percent increase in the xanthophyll content of dehydrated Coastal bermudagrass increases its value in broiler rations by about $10 a ton and that the same percentage increase in its lysine content increases its value by only about $1 a ton (Figure 3). Such findings disclose that research on
Y. DAVIES, W. K. TROTTER AND D. BURDICK
106
Ration COST Cwt) 4.00
-
M.
3.95 3.90
/:•:••:•:••:•
:::
3.85 3.80
"
3.75 3.70 3.65
-
02
0,3
0.4
0.5
0.6
0.7
0.8
.. /.. 0.9
•••••>•••••
1.0
,:e. .'..-.•.
I.I
Lysine requirement ( Percent)
FIG. 4. Effect of different lysine requirements on cost of the broiler finisher ration.
that are cheap to meet. The findings of P.R.R. along with experimental feeding trials can result in more exact nutrient and nonnutrient requirements. Since this replaces the costly practice of formulating with excesses, more economical rations will be the end result. To illustrate parametric restriction ranging, the lysine requirement of the broiler finisher diet was ranged from 1.2 to 0.0 percent (Figure 4). At the same time, all other coefficients remained constant so that any change in ration cost or composition would be associated with changes in the lysine requirement only. Relaxing the lysine minimum from 1.1 percent recommended by the National Research Council to 1.0 percent reduced the cost of the ration by $1.80 a ton. Further reductions resulted in successively cheaper rations—up to a point; however, reducing the lysine requirement below 0.7 percent neither changed the cost of the ration nor the blend of ingredients. LIMITATIONS In conclusion, any technique of this type
must be used with caution. Computers give a mathematically accurate feed formula calculated from estimated nutrition data, but the quality of the solution is only as reliable as the input data. To obtain a solution the problem must be quantified and specific values assigned to coefficients in the matrix. This is why it is important to have, whenever possible, composition data that reflect biological availability of nutrients. Another consideration is that the solutions to linear programming problems are static, having been based on a single set of prices. Even with parametrics, all prices are held constant except for prices of the traced ingredients. Finally, linear and parametric programming operate under the assumption of linearity. In some cases interactions between ingredients may result in nonlinear relationships. REFERENCES Dent, J. B., and H. Casey, 1967. Linear Programming and Animal Nutrition. J. B. Lippincott Co., Philadelphia, Pa. Enochian, R. V., G. O. Kohler and D. D. Kuzmicky, 1971. Evaluating research improvements
Downloaded from http://ps.oxfordjournals.org/ by guest on May 7, 2015
3.60
107
LINEAR PROGRAMMING EVALUATION OF FEEDS on livestock feeds through parametric linear programming. Cereal Science Today, 16(6): 181-189. Frazer, J. R., 1968. Applied Linear Programming. Prentice-Hall, Inc., Englewood Cliffs, N.J. Harvey, D., 1970. Tables of the Amino Acids in Foods and Feedingstuffs. Technical Communication No. 19. Commonwealth Agricultural Bureaux, Farnham Royal, Bucks, England. Institute of Food and Agricultural Sciences at the University of Florida, 1969. Proceedings of a Seminar: An evaluation of animal nutrition data used in the computer formulation of rations. Gainesville, Fla. National Research Council, 1971. Nutrient Requirements of Poultry. National Academy of
Sciences Printing and Publishing Office, Washington, D.C. Parkhurst, R. T., 1967. Commercial Broiler Production. Agricultural Handbook 320. Government Printing Office, Washington, D.C. Stafford, L. H., L. E. Ott and L. C. Snyder, 1965. Managerial aspects of least-cost feed formulation with linear programming. Marketing Research Report No. 729. Government Printing Office, Washington, D.C. Taylor, R. D., G. O. Kohler, K. H. Maddy and R. V. Enochian, 1968. Alfalfa meal in poultry feeds—an economic evaluation using parametric linear programming. Agricultural Economic Report No. 130. Government Printing Office, Washington, D.C.
1. P H , RATE OF ACID PENETRATION INTO EGG COMPONENTS AND BACTERIOLOGICAL ANALYSES1 J. C. ACTON AND M. G. JOHNSON Department of Food Science, Clemson University, Clemson, South Carolina 29631 (Received for publication April 7, 1972)
ABSTRACT The white and yolk components of hard cooked eggs pickled in 3 % or 5% acetic acid vinegars reached nearly equal pH values of 4.0-4.1 within six days after preparation. The pH declined rapidly in the egg white with a slower decrease occurring in the yolk. Maximal acetic acid concentrations were attained in the white in one day. Complete penetration of acid through the white to the yolk required 3 to 6 days to reach an equilibrium concentration and was dependent on the initial acid strength of the pickling solution. From day 6 to day 15, only slight changes in pH or acid concentration of the pickling solution, white or yolk were noted. Pickling spice ingredients reduced the initial acid strength of the pickling media ( 3 % or 5%) by 20-23%. Bacteriological analyses of pickling solutions indicate that the pickled eggs were bacteriologically safe. POULTRY SCIENCE 52:
INTRODUCTION
OTUDIES of hard cooked eggs have ^ been conducted to evaluate the correlation of initial egg quality and method of cooking with peeling problems (Swanson, 1959; Meehan et al., 1961; Reinke and Spencer, 1964; Fuller and Angus, 1959; Irmiter et al., 1970). In general, storage 1
Technical Contribution No. 1001 of the South Carolina Agricultural Experiment Station, Clemson University, Clemson, S.C. 29631.
107-111,
1973
conditions, pH of the egg albumen and cooking method were directly related to the cooked egg's peelability. Hard cooked eggs when packaged exude liquid with a greenish yellow tint. Chemical analysis of exudate (Nath et al., 1971) showed components which appeared to originate solely from the egg white. Baker et al. (1967) examined factors affecting the discoloration of hard cooked egg yolk. The yolk pH, high cooking temperature, long cooking time and long storage
Downloaded from http://ps.oxfordjournals.org/ by guest on May 7, 2015
Pickled Eggs
POULTRY SCIENCE 52:
INTRODUCTION
102-107,
1973
has another role not as widely known or EED represents the largest single cost used—the planning and economic evaluaitem in the production of poultry. Feed tion of research on new or improved feedaccounts for 62 percent of broiler produc- stuffs. This function is most successfully tion costs (Parkhurst, 1967). Minimizing performed by employing parametric linear feed costs through more efficient use of programming. Three parametric techavailable feedstuffs, therefore, is an impor- niques useful in research on feedstuffs are tant goal of all producers. In recent years described and illustrated in this paper. As a brief review, linear programming is the most effective means of attaining this goal has been the use of computers and lin- a mathematical procedure which solves a ear programming to formualte rations that series of linear equations simultaneously. meet the animal's nutritional requirements There are two essential steps in linear proat the lowest cost. This is now a widely ac- gramming. The first step is construction of cepted practice in the feed industry, with a mathematical model that represents the about 70 percent of the mixed feed in the problem to be solved. In ration formulation United States today being formulated by this involves setting up a matrix with rows computer (Enochian et al., 1971). Linear of constraints and columns of feed compoprogramming, by its rapid formulation of sition data. Diet requirements prescribe the economical and well-balanced rations, has constraints to be considered and include established its role as an important tool in both nutrient and nonnutrient elements. feed manufacturing. Linear programming Nutrient restrictions might be minimums and/ or maximums for protein, calcium, vi"Agricultural Research Service, Richard B. tamin A, metabolizable energy, etc. NonnuRussell Agricultural Research Center, Forage and trient restrictions might be pelletability or Feed Laboratory, Athens, Georgia 30604. palatability factors. The second step is so2 Economic Research Service, Richard B. Russell lution of the problem. This involves formuAgricultural Research Center, Liaison Group, lating that blend of ingredients which Athens, Georgia 30604.
F
102
Downloaded from http://ps.oxfordjournals.org/ by guest on May 7, 2015
ABSTRACT The use of linear programming and computers to formulate rations that meet the nutritional requirements of poultry at lowest cost is a widely accepted practice in the poultry feed industry. One application of linear programming not readily employed by poultry nutritionists is the use of parametric linear programming in the planning and economic evaluation of research on new or improved feedstuffs. Three parametric techniques useful in research are parametric cost ranging, parametric nutrient ranging, and parametric restriction ranging. Parametric cost ranging is useful in evaluating the market potential for new or improved feedstuffs and examining competitive and substitution relationships among ingredients. Parametric nutrient ranging, by analyzing at different levels the nutrient content of a particular feed ingredient, shows the changes in economic value that result from changes in the ingredient's nutrient composition. Parametric restriction ranging enables one to analyze the effect of changes in dietary requirements on ration cost and composition and to identify those nutrients for which diet requirements need to be more precisely denned.
LINEAR
PROGRAMMING EVALUATION OF FEEDS
PARAMETRIC COST RANGING Parametric cost ranging involves ranging the price of one or more ingredients while prices of other ingredients are held constant. Many ingredient prices can be ranged simultaneously, but the association of cause and effect is difficult when several cost factors are ranged. When an ingredient price is parameterized, P.C.R. shows the quantity of the traced feed ingredient which will be used in the least-cost ration at various price levels. This essentially gen-
Price ($/cwt)
0.50 K, ... Quantity in ration (Percent)
FIG. 1. Economic value curve for sunflower expeller meal in broiler finisher rations.
erates a steplike demand function for the traced ingredient (Figure 1). Such a curve gives the highest price at which the traced ingredient enters the ration and the increase in usage at successively lower prices. In this way, the economic value or nutritive worth of a particular feedstuff is quantified and an estimate of its potential market demand at different price levels can be made. The value will depend on the ingredient's nutrient composition and nutrient availability (if known), the composition and price of other ingredients, 3 diet requirements, and any bounds imposed on feed ingredients. When sunflower expeller meal 4 1 % was evaluated in broiler finisher rations, it had 'Feed ingredient prices used in this analysis were average prices for June 1971 and included all feedstuffs available on the Atlanta, Georgia, market.
Downloaded from http://ps.oxfordjournals.org/ by guest on May 7, 2015
meets diet requirements at the least cost. Selection among all available feedstuffs is based on the premise that feeds are interchangeable on a nutritional basis and is dependent upon complete and accurate composition data for all ingredients to be considered. Parametric linear programming is a refinement or sophistication of linear programming. Parametric programming traces the changes in the solution to a linear programming problem as one or more of the coefficients vary. I n this way flexibility is added to linear programming's rigid structure. The value of one or more coefficients in a row, column, or combination of row and column can be varied over a specified range. These coefficients can be prices of ingredients, nutrient content of ingredients, or diet requirements. Usually only one coefficient is parameterized (analyzed at different levels) while all other coefficients remain fixed. Whether the ranged coefficient is the cost of an ingredient, nutrient content of an ingredient, or diet restriction determines the name of the procedure. These are termed parametric cost ranging (P.C.R.), parametric nutrient ranging (P.N.R.), and parametric restriction ranging (P.R.R.), respectively. Each of these procedures will be discussed in terms of their role in the planning and economic evaluation of research on poultry feedstuffs.
103
104
Y. DAVIES, W. K. TROTTER AND D. BURDICK
Price ($/cwt)
15
20
25
Fie. 2. Economic value curves for sunflower expeller meal in three poultry diets.
a nutritive worth of $4.50 a hundredweight or $90 a ton. Results of the analysis are presented in Figure 1. At $90 a ton, sunflower meal forms 2 percent of the leastcost ration (Point A). This represents the first step of the discontinuous function. Sunflower meal increases to 6 percent of the ration if the price drops to $88 a ton (Point B). Further increases in usage occur at prices of $60, $58, and $14 a ton. However, since these are considerably below the selling price of $85 a ton, Points C, D, and E are of academic interest only. Parametric cost ranging is particularly useful when (1) developing a new ingredient or improving the quality of a known ingredient and an indication of its economic feasibility is required, (2) evaluating a new ingredient of known composition which has been introduced to the industry—as in the case of sunflower meal, (3) evaluating an ingredient in different rations or for feeding
TABLE 1.—A mino acid composition of sunfloiver meal 41%, soybean meal 44%, and egg protein Amino acid
Arginine Histidine Isoleucine Leucine Lysine Methionine Phenylalanine Threonine Tryptophan Valine
Sunflower meal 4 1 %
Soybean meal 44%
Egg protein
%
%
%
4.2 1.1 2.4 3.0 2.0 1.6 2.4 1.6 0.6 2.4
3.2 1.1 2.5 3.4 2.9 0.6 2.2 1.7 0.6 2.4
4.8 1.5 4.2 6.5 5.4 2.9 4.2 3.9 1.0 6.5
Downloaded from http://ps.oxfordjournals.org/ by guest on May 7, 2015
10
Quantity in ration (Percent)
to different species, (4) evaluating an ingredient on the basis of cost relationships at different market locations, and (5) evaluating competitive relationships among substitute ingredients. Another illustration of P.C.R.'s use in research is provided in Figure 2 where sunflower meal is evaluated for use in different poultry rations. In all three rations sunflower meal 4 1 % substitutes for soybean meal 44%. As shown in Table 1, lysine is sunflower's most limiting amino acid, but its high methionine content compared to soybean meal and other feed ingredients makes it valuable in poultry rations. Highest acceptance prices for the meal are $110, $90, and $86 a ton in the layer, broiler finisher, and broiler starter rations, respectively. Sunflower meal seems to have a greater potential as a protein supplement for layers than for broilers since at the market price it constitutes 13 percent of the least-cost layer ration, 6 percent of the broiler finisher ration, and 1 percent of the broiler starter ration. In these analyses, all input data were identical with the exception of diet requirements; therefore, any differences in valuation of the meal are due to differences in requirements. One factor that accounts for sunflower meal's superior showing in the layer diet is that layers, being more mature and having a greater di-
LINEAR PROGRAMMING EVALUATION OF FEEDS
gestive tract capacity than broilers, can accommodate more fiber in the ration; sunflower meal contains 13 percent crude fiber while soybean meal contains 7 percent fiber. Maximum limits on fiber in the poultry rations are 3.5 percent in the broiler starter diet, 4.0 percent in the broiler finisher diet, and 5.0 percent in the layer diet.
105
Increase in economic value ($/ton)
PARAMETRIC NUTRIENT RANGING
Increase in nutrient content (Percent)
FIG. 3. Relationship between improving the nutrient content of Coastal bermudagrass for broilers and increasing its economic value.
the improvement of Coastal's xanthophyll content would be more valuable dollarwise. Of course, any improvement in quality must be weighed against the added cost of processing to achieve this improved quality. PARAMETRIC RESTRICTION RANGING Parametric restriction ranging enables one to analyze at different levels the dietary requirement for a particular nutrient or nonnutrient. One or more requirements can be ranged simultaneously, but it is most beneficial to analyze a single requirement. P.R.R. shows the changes in ration cost and composition that occur when a given diet requirement is relaxed or tightened. From an examination of the cost of each diet restriction and the critical points at which these costs change, the nutritionist can identify those areas most in need of nutrition research. In this sense, P.R.R. can serve as a guide to determine where research priorities should be placed. Research should be conducted to narrow the safety margins on the costly diet restrictions, whereas research effort need not be expended on precisely defining requirements
Downloaded from http://ps.oxfordjournals.org/ by guest on May 7, 2015
Parametric nutrient ranging involves analyzing at different levels the nutrient content of a particular feed ingredient. P.N.R. shows the changes in economic value that the ingredient undergoes when its nutrient composition is improved or enhanced. Nutrients are assigned importance on the basis of their cost. Research efforts too should be directed to those areas where the greatest economic gain can be realized. Parametric nutrient ranging can help identify and establish priorities for the research needed to improve the nutritional value of feedstuffs. Parametrics can be of use in evaluating alternative research projects, especially in deciding on the best course of action when contemplating improvement in the nutrient content of an ingredient. The nutrient composition and nutrient availability of ingredients can be altered in many ways—by processing procedures, chemical or enzymatic modification, fermentation, storage and handling practices, time-of-harvest, or plant breeding. Using P.N.R. we can determine what alterations would be most beneficial in terms of cost and then initiate research to provide specific nutrients at a predetermined level. Results of a P.N.R. study indicate that a 10 percent increase in the xanthophyll content of dehydrated Coastal bermudagrass increases its value in broiler rations by about $10 a ton and that the same percentage increase in its lysine content increases its value by only about $1 a ton (Figure 3). Such findings disclose that research on
Y. DAVIES, W. K. TROTTER AND D. BURDICK
106
Ration COST Cwt) 4.00
-
M.
3.95 3.90
/:•:••:•:••:•
:::
3.85 3.80
"
3.75 3.70 3.65
-
02
0,3
0.4
0.5
0.6
0.7
0.8
.. /.. 0.9
•••••>•••••
1.0
,:e. .'..-.•.
I.I
Lysine requirement ( Percent)
FIG. 4. Effect of different lysine requirements on cost of the broiler finisher ration.
that are cheap to meet. The findings of P.R.R. along with experimental feeding trials can result in more exact nutrient and nonnutrient requirements. Since this replaces the costly practice of formulating with excesses, more economical rations will be the end result. To illustrate parametric restriction ranging, the lysine requirement of the broiler finisher diet was ranged from 1.2 to 0.0 percent (Figure 4). At the same time, all other coefficients remained constant so that any change in ration cost or composition would be associated with changes in the lysine requirement only. Relaxing the lysine minimum from 1.1 percent recommended by the National Research Council to 1.0 percent reduced the cost of the ration by $1.80 a ton. Further reductions resulted in successively cheaper rations—up to a point; however, reducing the lysine requirement below 0.7 percent neither changed the cost of the ration nor the blend of ingredients. LIMITATIONS In conclusion, any technique of this type
must be used with caution. Computers give a mathematically accurate feed formula calculated from estimated nutrition data, but the quality of the solution is only as reliable as the input data. To obtain a solution the problem must be quantified and specific values assigned to coefficients in the matrix. This is why it is important to have, whenever possible, composition data that reflect biological availability of nutrients. Another consideration is that the solutions to linear programming problems are static, having been based on a single set of prices. Even with parametrics, all prices are held constant except for prices of the traced ingredients. Finally, linear and parametric programming operate under the assumption of linearity. In some cases interactions between ingredients may result in nonlinear relationships. REFERENCES Dent, J. B., and H. Casey, 1967. Linear Programming and Animal Nutrition. J. B. Lippincott Co., Philadelphia, Pa. Enochian, R. V., G. O. Kohler and D. D. Kuzmicky, 1971. Evaluating research improvements
Downloaded from http://ps.oxfordjournals.org/ by guest on May 7, 2015
3.60
107
LINEAR PROGRAMMING EVALUATION OF FEEDS on livestock feeds through parametric linear programming. Cereal Science Today, 16(6): 181-189. Frazer, J. R., 1968. Applied Linear Programming. Prentice-Hall, Inc., Englewood Cliffs, N.J. Harvey, D., 1970. Tables of the Amino Acids in Foods and Feedingstuffs. Technical Communication No. 19. Commonwealth Agricultural Bureaux, Farnham Royal, Bucks, England. Institute of Food and Agricultural Sciences at the University of Florida, 1969. Proceedings of a Seminar: An evaluation of animal nutrition data used in the computer formulation of rations. Gainesville, Fla. National Research Council, 1971. Nutrient Requirements of Poultry. National Academy of
Sciences Printing and Publishing Office, Washington, D.C. Parkhurst, R. T., 1967. Commercial Broiler Production. Agricultural Handbook 320. Government Printing Office, Washington, D.C. Stafford, L. H., L. E. Ott and L. C. Snyder, 1965. Managerial aspects of least-cost feed formulation with linear programming. Marketing Research Report No. 729. Government Printing Office, Washington, D.C. Taylor, R. D., G. O. Kohler, K. H. Maddy and R. V. Enochian, 1968. Alfalfa meal in poultry feeds—an economic evaluation using parametric linear programming. Agricultural Economic Report No. 130. Government Printing Office, Washington, D.C.
1. P H , RATE OF ACID PENETRATION INTO EGG COMPONENTS AND BACTERIOLOGICAL ANALYSES1 J. C. ACTON AND M. G. JOHNSON Department of Food Science, Clemson University, Clemson, South Carolina 29631 (Received for publication April 7, 1972)
ABSTRACT The white and yolk components of hard cooked eggs pickled in 3 % or 5% acetic acid vinegars reached nearly equal pH values of 4.0-4.1 within six days after preparation. The pH declined rapidly in the egg white with a slower decrease occurring in the yolk. Maximal acetic acid concentrations were attained in the white in one day. Complete penetration of acid through the white to the yolk required 3 to 6 days to reach an equilibrium concentration and was dependent on the initial acid strength of the pickling solution. From day 6 to day 15, only slight changes in pH or acid concentration of the pickling solution, white or yolk were noted. Pickling spice ingredients reduced the initial acid strength of the pickling media ( 3 % or 5%) by 20-23%. Bacteriological analyses of pickling solutions indicate that the pickled eggs were bacteriologically safe. POULTRY SCIENCE 52:
INTRODUCTION
OTUDIES of hard cooked eggs have ^ been conducted to evaluate the correlation of initial egg quality and method of cooking with peeling problems (Swanson, 1959; Meehan et al., 1961; Reinke and Spencer, 1964; Fuller and Angus, 1959; Irmiter et al., 1970). In general, storage 1
Technical Contribution No. 1001 of the South Carolina Agricultural Experiment Station, Clemson University, Clemson, S.C. 29631.
107-111,
1973
conditions, pH of the egg albumen and cooking method were directly related to the cooked egg's peelability. Hard cooked eggs when packaged exude liquid with a greenish yellow tint. Chemical analysis of exudate (Nath et al., 1971) showed components which appeared to originate solely from the egg white. Baker et al. (1967) examined factors affecting the discoloration of hard cooked egg yolk. The yolk pH, high cooking temperature, long cooking time and long storage
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Pickled Eggs