document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191132>Question 1191132</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A manufacturer produces three​ products, A,​ B, and C. The profits for each unit of​ A, B, and C sold are ​$​1, ​$2​, and ​$3​, respectively. Fixed costs are ​$19000 per​ year, and the costs of producing each unit of​ A, B, and C are ​$​4, ​$5, and ​$​7, respectively. Next​ year, a total of 11,000 units of all three products is to be produced and​ sold, and a total profit of ​$25,000 is to be realized. If total cost is to be ​$82,000​, how many units of each of the products should be produced next​ year? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #822903 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=822903\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x is the number of units of product A.<BR>\n" );
document.write( "y is the number of units of product B.<BR>\n" );
document.write( "z is the number of units of product C<BR>\n" );
document.write( "your objective function is:<BR>\n" );
document.write( "profit = 1x + 2y + 3z = 25000<BR>\n" );
document.write( "costs = 19000 + 4x + 5y + 7z = 82000<BR>\n" );
document.write( "number of units to be produced and sold = x + y + z = 11000<BR>\n" );
document.write( "you have 3 equations that need to be solved simultaneously.<BR>\n" );
document.write( "they are:<BR>\n" );
document.write( "1x + 2y + 3z = 25000<BR>\n" );
document.write( "19000 + 4x + 5y + 7z = 82000<BR>\n" );
document.write( "x + y + z = 11000<BR>\n" );
document.write( "after solving these 3 equations simultaneously, you get:<BR>\n" );
document.write( "x = 2000<BR>\n" );
document.write( "y = 4000<BR>\n" );
document.write( "z = 5000<BR>\n" );
document.write( "1x + 2y + 3z = 2000 + 8000 + 15000 = 25000<BR>\n" );
document.write( "19000 + 4x + 5y + 7z = 19000 + 8000 + 20000 + 35000 = 82000<BR>\n" );
document.write( "x + y + z = 2000 + 4000 + 5000 = 11000<BR>\n" );
document.write( "this confirms the solution is correct.<BR>\n" );
document.write( "the solution is:<BR>\n" );
document.write( "2000 units of product A and 4000 units of product B and 5000 units of product C need to be produced and sold to get a profit of 25000 at a total cost of 82000.\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "if you need to know to solve the 3 equations simultaneously, let me know and i'll go through it with you.<BR>\n" );
document.write( "let me know if you have any other questions or concerns as well.<BR>\n" );
document.write( "theo\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );