I need to find the combination of two ingredients out of four given that will give me a 18% by weight protein content at 20 tons. The ingredients are:
Barley- 11% protein, $131.81 a ton,
Corn- 9% protein, $133.63 a ton
Cottonseed meal- 41% protein, $257.00 a ton
Soybean meal- 48% protein, $301.00 a ton.
What equations do I setup that let me find the combinations?
Do I need to try all different combinations or can I use less equations. I can only use two different ingredients to reach the desired 18% protein at 20 tons.
You need one ingredient that is more than $18\%$ protein and one that is less, so there are only four combinations to try. Compute the total amount of protein that you need. Then if you have $x$ of one ingredient and $20-x$ of the other, compute $x$ to get that much protein. You can use that to compute the total cost of the mix.