Algebra.Com's Answer #828808 by ikleyn(52790)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
.
\n" );
document.write( "A firm can produce three types of cloths A, B and C.
\n" );
document.write( "Three kinds of wool are required for it, say red, green and blue wool. \r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "One unit of type ‘A’ cloth needs 2 yards of red, 8 yards of green and 1 yard of blue wool; \r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "one unit of type ‘B’ cloth needs 1 yard of red, 3 yards of green and 5 yards of blue wool; \r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "one unit of type ‘C’ cloth needs 6 yards red, 2 yards of green and 1 yard of blue wool. \r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "The firm has only a stock of 9 yards red, 13 yards green and 7 yards of blue wool.
\n" );
document.write( "If total stock is used, then write mathematical formulation of the problem and determine
\n" );
document.write( "the number of units of the three type’s cloth A, B and C to be produced by using Gauss
\n" );
document.write( "Elimination method
\n" );
document.write( "~~~~~~~~~~~~~~\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "\r\n" );
document.write( "Let x be the number of units A; y be the number of units B, and z be the number of units C.\r\n" );
document.write( "\r\n" );
document.write( "Write a system of linear equations as you read the problem.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " A kind advise is to format the textual description  as I did in my post for easy reading.\r\n" );
document.write( " Some teachers advise to create a Table to facilitate your work.\r\n" );
document.write( "\r\n" );
document.write( " To be honest, in my life I solved tens such problems,\r\n" );
document.write( " but NEVER created any table (considering it as useless spending of valuable time . . . )\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "In any case, the system is as you see it below\r\n" );
document.write( "You simply write a balance for each type of source separately, and place coefficients \r\n" );
document.write( "in equations as you see appropriate numbers in the problem's description.\r\n" );
document.write( "\r\n" );
document.write( " 2x + 1y + 6z = 9 (red) (1)\r\n" );
document.write( "\r\n" );
document.write( " 8x + 3y + 2z = 13 (green) (2)\r\n" );
document.write( "\r\n" );
document.write( " 1x + 5y + 1z = 7 (blue) (3)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "As soon as the system is ready, the setup is done.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now I should solve this system.\r\n" );
document.write( "Notice, that we MUST seek for solutions in non-negative INTEGER NUMBERS, only.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The problem asks to solve the system by the Elimination method.\r\n" );
document.write( "But, would I start do it, other people could think that I am slow stupid person.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From equations, it is CLEARLY SEEN, that\r\n" );
document.write( "\r\n" );
document.write( " x = 1 (from equation (2), it can not be an integer number greater than 1);\r\n" );
document.write( "\r\n" );
document.write( " y = 1 (from equation (3), it can not be an integer number greater than 1);\r\n" );
document.write( "\r\n" );
document.write( " z = 1 (from equation (1), it can not be an integer number greater than 1).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "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).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It is easy: you can do it on your own, and I leave it to you.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER. 1 unit of A; 1 unit of B and 1 unit of C.\r\n" );
document.write( " \r
\n" );
document.write( "\n" );
document.write( "Solved.\r
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "////////////////\r
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "Notice that in your post, I  couple of words that mistakenly got there due to unknown cause\r
\n" );
document.write( "\n" );
document.write( "(probably, due to somebody's inaccuracy . . . )\r
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "Unnecessary words in any Math problem's description do not help to understand and solve it,
\n" );
document.write( "so they must be thoroughly filtered out.\r
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "I know this wisdom from my years of childhood . . . \r
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( " \n" );
document.write( " |