- #1
sdoug041
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Homework Statement
Your doctor has asked you to take 5 units of vitamin A, 13 units of Vitamin B, and 23 units of vitamin C every day. There are three brands available in your local pharmacy which contain the following units of vitamins:-------- vitamin A vitamin B vitamin C
Brand 1 --- 1 ------ 2 ------ 4
Brand 2 --- 1 ------ 1 ------ 3
Brand 3 --- 0 ------ 1 ------ 1
Find all combinations of pills that provide you with the exact daily requirement (no partial pills!).
Homework Equations
Gaussian algorithm / elimination
The Attempt at a Solution
I transposed to create an augmented matrix in which the required amount of each pills could be implemented in the matrix.
ie
---------------Brand 1--------Brand 2-------Brand 3 ------Total
Vitamin A --------1 --------------1 -----------0 -----------5
Vitamin B --------2 --------------1 -----------1 ---------- 13
Vitamin C ------- 4 --------------3 -----------1 ----------23
I tried to use Gaussian Algorithm to solve for each variable but I keep eliminating all the values in row 3 (ie 0 0 0 0). I do believe this implies infinite solutions, but obviously this cannot be true. Please help!
Thanks,
Steve