March 30 2016 TO: Augustine Mok FROM: Ruojia Li RE: Least Cost Dairy Ration Since you are going to make plans of feed ingredient procurement for the coming month, you have asked me to help identify a least feed ingredient’s cost ration for cows with some requirements. Then I also need to do some sensitivity analysis based on the market trend and the variable factors. In detail, the feed ingredients include alfalfa hay (AH), cracked corn grain (CG), dried distillers grains (DDG), soybean meal (SMEAL), corn silage (CS) and wheat middlings (WMIDDS). And the requirements include nutrient provided requirements for each cow and amount requirements of some feed ingredients. In this repot, I am using the data from National Research Council for ensuring daily maintenance and milk production nutrient requirements. In additional, the cost and nutrient content of these feed ingredients are determined in advance. All the information is listed in the tables below: Nutrient Requirements Total digestible nutrients,TDN (lbs) 29.8 Total crude protein, TCP (lbs) 6.71 Calcium (lbs) 0.259 Phosphorous, Phos (lbs) 0.16 Vitamin A (International Units, IU) 41 Roughage (lbs) 22.5 Feed Ingredient Abbreviation AH CG DDG SMEAL CS WMIDDS Cost per pound ($) 0.1450 0.0710 0.1150 0.2295 0.0000 0.0825 Nutrient (lbs.) : TDN 0.50 0.80 0.78 0.74 0.20 0.76 TCP 0.170 0.086 0.270 0.480 0.024 0.160 Calcium 0.0140 0.0002 0.0009 1.4600 0.0009 0.0030 Phos 0.0020 0.0030 0.0036 3.0300 0.0006 0.0065 Vitamin A 13.90 0.34 0.00 0.00 2.86 0.00 Roughage 0.90 0.00 0.00 0.00 0.35 0.00 Additional Amount Requirements Less than CG Ready, can be pro- -vided 12 lb./day only No more than 5 lb./day For this analysis, I build a basic linear programming model with six nutrient demand requirements and three additional amount requirements. The basic model aims to find the least total cost satisfying all the constraints on those requirements. And this model is attached as the Table 1. The solution to the model is presented in the Table 2. At the first, in the Answer Report, the least total feed cost per cow per day is about $4.73, which is under the “Objective cell”. Then, the amounts (final values) of each kind of feed ingredient are under the “Variable cells”. For achieving the least cost every day, every cow needs 20.33 lbs alfalfa hay (AH), 13.02 lbs cracked corn grain (CG), 3.86 lbs dried distillers grains (DDG), 0.009 lbs soybean meal (SMEAL), 12 lbs corn silage (CS) and 5 lbs wheat middlings (WMIDDS). Next, in the module
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