You are an entrepreneur starting a company to sell vitamin supplements. In manufacturing you have a bioreactor that has three input streams and one output stream. Each input vessel is carrying two vitamins. The first input stream is a slurry of Vitamins A and B12 in water. Stream 2 is a slurry of Vitamins B12 and C in water. Stream 3 is a slurry of Vitamins C and D in water. The output stream is a slurry with all 4 vitamins that goes down stream in your production to be formed into gel caplets. Each slurry input is 1 part the first vitamin, 1 part the second vitamin, and 1 part water. If the downstream processes in your manufacturing can only handle up to 100 gm/hr of the output flow, determined the flow rates of the input streams that will maximize production if your output needs to be (10+a)% Vitamin D and (20+b)% Vitamin C. What percentages of your output slurry would be Vitamin A and Vitamin B12?
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