SOLUTION: To produce sausage formulations, packers normally use lean beef, pork belly, and soy concentrate. The manufacturer uses 3 percent soy in final sausage mass. Water is added to the

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Question 835994: To produce sausage formulations, packers normally use lean beef, pork belly, and soy concentrate. The manufacturer uses 3 percent soy in final sausage mass. Water is added to the formulation as ice. The final sausage must contain: 15 percent protein, 60 percent moisture, and 25 percent fat. The ingredients contain the following:
lean beef- 20% protein, 67% moisture, 13% fat
pork belly- 10% protein, 40 % moisture, 50% fat
soy- 90% protein, 7% moisture, 0% fat
How much of each ingredient should be combined to make 600 kg of sausage emulsion?
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
b beef
p pork
y soY
w water as ice

b%2Bp%2By%2Bw=600


Account for Protein: 0.2b%2B0.1p%2B0.9y%2B0%2Aw=0.15
Account for Moisture: 0.67b%2B0.4p%2B0.07y%2B1%2Aw=0.60
Account for Fat: 0.13b%2B0.5p%2B0%2Ay%2B0%2Aw=0.25

This is a linear system of four equations in four unknown variables. The ingredient accounting equations should be adjusted so whole number coefficients. You would probably choose to use matrix operations to solve the system. ( I myself would try to use some on-line matrix software to handle the system, like the one through purdue ).