Question 1196098: A firm can produce three types of cloths A, B and C. Three kinds of wool are required
for it, say red, green and blue wool. One unit of type ‘A’ cloth needs 2 yards of red
wool, 8 yards of green and one yard of blue wool; one unit  of type ‘B’ cloth
needs one yard of red, 3 yards of green and 5 yards of blue wool; one unit of
type ‘C’ cloth needs 6 yards red, 2 yards of green and one yard of blue wool. The firm
has only a stock of 9 yards red, 13 yards green and 7 yards of blue wool. If total stock
is used, then write mathematical formulation of the problem and determine the
number of units of the three type’s cloth A, B and C to be produced by using Gauss
Elimination method
Answer by ikleyn(52788)   (Show Source):
You can put this solution on YOUR website! .
A firm can produce three types of cloths A, B and C.
Three kinds of wool are required for it, say red, green and blue wool.
One unit of type ‘A’ cloth needs 2 yards of red, 8 yards of green and 1 yard of blue wool;
one unit of type ‘B’ cloth needs 1 yard of red, 3 yards of green and 5 yards of blue wool;
one unit of type ‘C’ cloth needs 6 yards red, 2 yards of green and 1 yard of blue wool.
The firm has only a stock of 9 yards red, 13 yards green and 7 yards of blue wool.
If total stock is used, then write mathematical formulation of the problem and determine
the number of units of the three type’s cloth A, B and C to be produced by using Gauss
Elimination method
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Let x be the number of units A; y be the number of units B, and z be the number of units C.
Write a system of linear equations as you read the problem.
A kind advise is to format the textual description  as I did in my post for easy reading.
Some teachers advise to create a Table to facilitate your work.
To be honest, in my life I solved tens such problems,
but NEVER created any table (considering it as useless spending of valuable time . . . )
In any case, the system is as you see it below
You simply write a balance for each type of source separately, and place coefficients
in equations as you see appropriate numbers in the problem's description.
2x + 1y + 6z = 9 (red) (1)
8x + 3y + 2z = 13 (green) (2)
1x + 5y + 1z = 7 (blue) (3)
As soon as the system is ready, the setup is done.
Now I should solve this system.
Notice, that we MUST seek for solutions in non-negative INTEGER NUMBERS, only.
The problem asks to solve the system by the Elimination method.
But, would I start do it, other people could think that I am slow stupid person.
From equations, it is CLEARLY SEEN, that
x = 1 (from equation (2), it can not be an integer number greater than 1);
y = 1 (from equation (3), it can not be an integer number greater than 1);
z = 1 (from equation (1), it can not be an integer number greater than 1).
The last step is to check that the triple (x,y,z) = (1,1,1) really is the solution, i.e. satisfies equations (1),(2) and (3).
It is easy: you can do it on your own, and I leave it to you.
ANSWER. 1 unit of A; 1 unit of B and 1 unit of C.
Solved.
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Notice that in your post, I  couple of words that mistakenly got there due to unknown cause
(probably, due to somebody's inaccuracy . . . )
Unnecessary words in any Math problem's description do not help to understand and solve it,
so they must be thoroughly filtered out.
I know this wisdom from my years of childhood . . .
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