SOLUTION: 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 componen

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

--
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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