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March 12th, 2015, 02:25 PM   #1
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Linear Systems Problem

Hi, this question was found in my calc 2 textbook and I'm not sure how to solve it.

Laboratory mice are fed with a mixture of two foods that contain two essential nutrients.
Food 1 contains 3 units of nutrient A and 2 units of nutrient B per ounce; food 2 contains 4 units of nutrient A and 5 units of nutrient B per ounce.
In what proportion should you mix the food if the mice require the nutrients A and B in equal amounts?
Assume now that the mice require the nutrients A and B in the ratio1 : 2.
Is it possible to satisfy their dietary needs with the two foods available?

any help would be greatly appreciated!! Thanks.
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March 12th, 2015, 03:31 PM   #2
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We want to mix the two feeds in some proportion $p:1$. So our food $F=pf_1 + f_2 = p(3A + 2B) + (4A + 5B)$. We require equal amounts of A and B. So$$3p + 4 = 2p + 5$$where the left hand side is the amount of A and the right hand side is the amount of B.
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March 12th, 2015, 07:37 PM   #3
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Originally Posted by v8archie View Post
We want to mix the two feeds in some proportion $p:1$. So our food $F=pf_1 + f_2 = p(3A + 2B) + (4A + 5B)$. We require equal amounts of A and B. So$$3p + 4 = 2p + 5$$where the left hand side is the amount of A and the right hand side is the amount of B.
Thanks so much!
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