How do I do this? I included a sample calculation of how we're supposed to do it. I've tried to do this a couple of times and its not making sense. Does the sucrose and corn syrup being liquid effect how this is calculated?

Desired: 400 kg of ice cream mix @ 14% fat, 10% msnf, 12% sucrose, 3% corn syrup solids, 0.2% stabilizer Available : Cream @ 36% fat; milk @ 3.9% fat; condensed skim milk @ 32% msnf; liquid sucrose @ 65% solids, liquid corn syrup @ 75% solids, stabilizer. Desired: 100 kg mix containing 18% fat, 9.5% milk solids-not-fat, 15% sucrose, 0.4% stabilizer, 1% frozen egg yolk. On hand: Cream 30% fat, milk 3.5% fat, skim milk powder 97% solids, sucrose, stabilizer, and egg yolk. Solution via the algebraic method: Sucrose: 100 kg mix 15 kg sucrose = 15 kg sucrose 100 kg mix Stabilizer: 100 kg mix 0.4 ke stabilizer = 0.4 kg 100 kg mix Egg yolk: 100 kg mix * 1 kg egg yolk = 1 kg egg yolk 100 kg mix Now, let x = skim powder, y = milk, z = cream. MASS BALANCE All the components add up to 100 kg x+y+z= 100 - (15+0.4 +1) MSNF BALANCE Equal to 9.5% of the mix and coming from the milk, the skim powder, and the cream; 0.97x+0.08685 y + 0.063 z = .095 (100) FAT BALANCE Equal to 18% of the mix and coming from the milk and cream .035 y + 3 z= .18 (100) x = 4.1 kg skim powder y = 22.1 kg milk z = 57.4 kg cream