Question 992432
A few details are described imprecisely but you have components to be mixed, in quantities x, y, and z for components 1, 2, and 3; in the order listed for the prices of each.


Accounting for material volumes, {{{x+y+z=60000}}}.


Accounting for material costs,  {{{2x+1.5y+1.25z=90000}}}.  You would want integer coefficients if possible, so multiply members by 4...
{{{8x+6y+5z=360000}}}.


Part of the description makes  {{{x/z=2}}}, giving {{{x=2z}}}.


The system of equations that can be best formed is
{{{system(x+y+z=60000,8x+6y+5z=360000,x-2z=0)}}}.


You could solve this using your gaussian or gauss-jordan row elimination method, but I wouldn't want to; I'd rather use the x=2z substitution and solve the resulting simpler system.


As the matrix, you can begin with  
{{{matrix(3,4,
1,1,1,60000,
8,6,5,360000,
1,0,-2,0)}}}


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I started solving on paper with pencil, and I am finding a meaningless result as one of the rows, like  ( 0 0 -3 0 ), indicating   z=0.  If my row operations are all correct, this would indicate that your materials can not all three be used to prepare the mixture described in your description.