document.write( "Question 1200628: A factory makes use of two basic machines, A and B, which turn out two different products, yarn and thread. Each unit of yarn requires 1 hour on machine A and 2 hours on machine B, while each unit of thread requires 1 hour on A and 1 hour on B. Machine A runs 8 hours per day, while machine B runs 14 hours per day. How many units each of yarn and thread should the factory make to keep its machines running at capacity? \n" ); document.write( "

Algebra.Com's Answer #834802 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "A factory makes use of two basic machines, A and B,
\n" ); document.write( "which turn out two different products, yarn and thread.
\n" ); document.write( "Each unit of yarn requires 1 hour on machine A and 2 hours on machine B,
\n" ); document.write( "while each unit of thread requires 1 hour on A and 1 hour on B.
\n" ); document.write( "Machine A runs 8 hours per day, while machine B runs 14 hours per day.
\n" ); document.write( "How many units each of yarn and thread should the factory make
\n" ); document.write( "to keep its machines running at capacity?
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document.write( "Let Y be the number of units of yarn, and\r\n" );
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document.write( "let T be the number of units of thread.\r\n" );
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document.write( "Write equations as you read the problem\r\n" );
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document.write( "    1*Y + 1*T =  8   hours   (machine A)     (1)\r\n" );
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document.write( "    2*Y + 1*T = 14   hours   (machine B)     (2)\r\n" );
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document.write( "     +--------------------------------+\r\n" );
document.write( "     |   Thus the setup is complete.  |\r\n" );
document.write( "     +--------------------------------+\r\n" );
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document.write( "To find Y, subtract eq(1) from eq(2).   You will get\r\n" );
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document.write( "    2Y - Y    = 14 - 8 = 6,  Y = 6.\r\n" );
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document.write( "Now find T from equation (1)\r\n" );
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document.write( "    T = 8 - Y = 8 = 6 = 2.\r\n" );
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document.write( "ANSWER.  6 units of yarn and 2 units of thread.\r\n" );
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