The problem involves determining the number of vitamin pills from three brands to meet specific daily requirements for vitamins A, B, and C. The context is set within the framework of Gaussian elimination to solve a system of equations represented by an augmented matrix.
There is an ongoing exploration of the relationships between the variables representing the number of pills from each brand. Some participants have provided guidance on defining variables and setting up equations, while others are questioning the validity of their results and the implications of their findings.
Participants note constraints related to the requirement for nonnegative whole numbers of pills and the implications of having three unknowns in two equations. There is also discussion about the limits on the values for the number of pills from brand 3 based on the equations derived from the matrix.
sdoug041 said:Ok I see.
If b3 >= 0 , and say b3 was indeed 0, then b2 would have to be -3 to satisfy the equation. Does this mean b3 should be 3<=b3<=8, and 0<=b1<= 5?
memomator said:The question states. Find all combination of pills that provide you with the exact daily requirement(no partial pill). How will I find all the combination of pills, knowing only the number of pills in brand 1, 2, and 3.
memomator said:Ok i understand that now, is there an easier way to find out how many solutions there are other than plugging into numbers.