document.write( "Question 1127215: A furniture factory manufactures two types of coffee table, A and B. Each coffee table goes through two distinct costing stages, assembly and finishing. The maximum capacity for assembly is 195 hours and for finishing, 165 hours. Each A table requires 4 hours assembly and 3 hours finishing, while a B table requires 1 hour for assembly and 2 hours for finishing. Calculate the number of A and B tables to be produced to ensure that the maximum capacity available is utilised \n" ); document.write( "

Algebra.Com's Answer #743620 by ikleyn(52803) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "The simplest and most straightforward way is to write the system of equations assuming that \r\n" );
document.write( "\r\n" );
document.write( "\"the maximum capacity available is utilized\" and then to check if it has solution/solutions in integer non-negative numbers.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "This system of equations is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "4*A + 1*B = 195  hours   (1)   (\"The maximum capacity for assembly  is 195 hours\")\r\n" );
document.write( "3*A + 2*B = 165  hours   (2)   (\"The maximum capacity for finishing is 165 hours\")\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Apply the Substitution or Elimination method - on your choice - to get the solution\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "A = 45,  B = 15.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Since the system has (admits) the solution in integer numbers, it is the \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Answer.  A = 45 and B = 15.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "You may check the answer on your own.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );