document.write( "Question 1203703: A furniture company makes dining room furniture. A buffet requires 40 hours for construction 10 hours for finishing. A chair requires 20 hours for construction and 20 hours for finishing. A table requires 40 hours for construction and 70 hours for finishing. The construction department has 500 hours of labor and the finishing department has 200 hours of labor available each week. How many pieces of each type of furniture should be produced each week if the factory is to run at full capacity? \n" ); document.write( "

Algebra.Com's Answer #839485 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "A furniture company makes dining room furniture.
\n" ); document.write( "A buffet requires 40 hours for construction 10 hours for finishing.
\n" ); document.write( "A chair requires 20 hours for construction and 20 hours for finishing.
\n" ); document.write( "A table requires 40 hours for construction and 70 hours for finishing.
\n" ); document.write( "The construction department has 500 hours of labor
\n" ); document.write( "and the finishing department has 200 hours of labor available each week.
\n" ); document.write( "How many pieces of each type of furniture should be produced each week if the factory is to run at full capacity?
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document.write( "X buffets; Y chairs; Z tables.\r\n" );
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document.write( "Write equations for full capacity as you read the problem\r\n" );
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document.write( "    40X + 20Y + 40Z = 500  hours   (1)   (the construction department time)\r\n" );
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document.write( "    10X + 20Y + 70Z = 200  hours   (2)   (the finishing department time)\r\n" );
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document.write( "Simplify equations by dividing each term by 10\r\n" );
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document.write( "    4X + 2Y + 4Z = 50     (1')  \r\n" );
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document.write( "     X + 2Y + 7Z = 20     (2')  \r\n" );
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document.write( "From equation (2'), Z may have only three possible values:      Z = 0,  or  1,  or  2.\r\n" );
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document.write( "If Z= 0, then equations (1'), (2') take the form\r\n" );
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document.write( "    4X + 2Y = 50\r\n" );
document.write( "     X + 2Y = 20\r\n" );
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document.write( "and have a UNIQUE solution X= 10, Y= 5.   (You can use the Elimination method to get this solution).\r\n" );
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document.write( "If Z= 1, then equations (1'), (2') take the form\r\n" );
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document.write( "    4X + 2Y = 46\r\n" );
document.write( "     X + 2Y = 13\r\n" );
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document.write( "and have a UNIQUE solution X= 11, Y= 1.  (You can use the Elimination method to get this solution).\r\n" );
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document.write( "If Z= 2, then equations (1'), (2') take the form\r\n" );
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document.write( "    4X + 2Y = 42\r\n" );
document.write( "     X + 2Y =  6\r\n" );
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document.write( "and have NO a solution in integer non-negative numbers.\r\n" );
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document.write( "Thus the problem has two possible solutions:  (X,Y,Z) = (10,5,0)  and/or  (X,Y,Z) = (11,1,1).\r\n" );
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document.write( "There are no other solutions.\r\n" );
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