A farming cooperative mixes two brands of cattle feed. Brand X costs $25 per bag

Question

A farming cooperative mixes two brands of cattle feed. Brand X costs $25 per bag and contains 2 units of nutritional element A, 2 units of elements B, and 2 units of element C. Brand Y costs $20 per bag and contains 1 unit of nutritional element A, 9 units of element B, and 3 units of element C. Find the number of bags of each brand that should be mixed to produce a mixture having a minimum cost per bag. The requirements of nutrients A, B, and C are 12 units, 36 units, and 24 units, respectively.

Explanation / Answer

This is a system of linear equations 2A + 1A = 12 2B + 9B = 36 2C +3B = 24 Let first column be vector x second column vector y and thesolution b cx + dy = b need to find c and d You will find that the closest you can get through row reduction isto let c = 9/2 and d=3 This solves the first two equations, but not the last. Infact you will get the row reduction you get 0 = 1 which translates to 0C + 0C = 1C This of course is an inconsistency since 0 does not equal 1. Meaning there is no solution to this question. It makes sensesince the vectors including your solution vector is linearlyindependent, this is no linear combination that will equal thesolution vector. there is no answer

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