Question 992432: CAN ANY ONE SOLVE IT BY GAUSSIAN ELIMINATION METHOD?
A blending process is to combine three components in such a way as to create a final blend of 60000 gallons.The three components cost $2.00,$1.50 and $1.25 per gallon respectively.Total cost of components should equal $90000.Another requirement in the blending is that the number of gallon used of component 1 should be twice the amount used of component 3.determine whether there is a combination of the three components which will lead to a final blend of 60000 gallon costing $90000 and satisfying the blending restrictions
kindly help
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website! 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,  .
Accounting for material costs,  . You would want integer coefficients if possible, so multiply members by 4...
 .
Part of the description makes  , giving  .
The system of equations that can be best formed is
 .
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
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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.
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