document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=240187>Question 240187</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A company designs and sells two types of rings:  the VIP and the SST.  The company can produce up to 24 rings each day using up to 60 total hours of labor.  It takes 3 hours to make one VIP ring, and 2 hours to make one SST ring.  How many of each type of ring should be made daily in order to maximize profit, if profit on a VIP ring is $30 and profit on an SST ring is $40?  What is the profit?\r<BR>\n" );
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document.write( "So far I have come up with this not sure if its correct?<BR>\n" );
document.write( "x=# of rings to VIP<BR>\n" );
document.write( "y=# of rings to SST\r<BR>\n" );
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document.write( "3x+2y< or equal to 60<BR>\n" );
document.write( "x+y< or equal to 2<BR>\n" );
document.write( "      \r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #176053 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=176053\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A company designs and sells two types of rings: the VIP and the SST. <BR>\n" );
document.write( "The company can produce up to 24 rings each day using up to 60 total hours of labor. It takes 3 hours to make one VIP ring, and 2 hours to make one SST ring. How many of each type of ring should be made daily in order to maximize profit, if profit on a VIP ring is $30 and profit on an SST ring is $40? What is the profit? <BR>\n" );
document.write( "So far I have come up with this not sure if its correct?<BR>\n" );
document.write( "x=# of rings to VIP<BR>\n" );
document.write( "y=# of rings to SST <BR>\n" );
document.write( "3x+2y< or equal to 60<BR>\n" );
document.write( "x+y< or equal to 24<BR>\n" );
document.write( "Profit = 30x+40y<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "Graphs:<BR>\n" );
document.write( "3x+2y <= 60<BR>\n" );
document.write( "y <= (-3/2)x + 30<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "x+y <= 24<BR>\n" );
document.write( "y <= -x+24<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-10%2C40%2C-10%2C40%2C%28-3%2F2%29x%2B30%2C-x%2B24%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-10%2C40%2C-10%2C40%2C%28-3%2F2%29x%2B30%2C-x%2B24%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Find the intersection of the two boundary lines:<BR>\n" );
document.write( "-x+24 = (-3/2)x+30<BR>\n" );
document.write( "(1/2)x = 6<BR>\n" );
document.write( "x = 12 so y = 12<BR>\n" );
document.write( "========================<BR>\n" );
document.write( "Check (0,0),(0,24),(20,0), (12,12) in the profit equation to determine the max pair.<BR>\n" );
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document.write( "Profit = 30x+40y<BR>\n" );
document.write( "P(0,0)=0 ; P(0,24)=40*24=960;P(20,0)=30*20=600;P(12,12)=30*12+40*12 = 840<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Max comes from x = 0, y = 24<BR>\n" );
document.write( "====================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );