document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=79587>Question 79587</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST.  They can produce up to 24 rings each day using up to 60 total man-hours of labor.  It takes 3 man-hours to make one VIP ring and 2 man-hours to make one SST ring.  How many of each type of ring should be made daily to maximize the company's profit, if the profit on a VIP ring is $40 and on an SST ring is $35? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #57168 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=57168\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24 rings each day using up to 60 total man-hours of labor. It takes 3 man-hours to make one VIP ring and 2 man-hours to make one SST ring. How many of each type of ring should be made daily to maximize the company's profit, if the profit on a VIP ring is $40 and on an SST ring is $35?<BR>\n" );
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document.write( "Let x = number of VIP rings: let y = number of SST rings<BR>\n" );
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document.write( "The total production inequality;<BR>\n" );
document.write( "x + y =< 24<BR>\n" );
document.write( "y = 24 - x; arranged to plot graph (purple)<BR>\n" );
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document.write( "The labor inequality;<BR>\n" );
document.write( "3x + 2y =< 60<BR>\n" );
document.write( "2y = 60 - 3x<BR>\n" );
document.write( "y = 60/2 - (3/2)x<BR>\n" );
document.write( "y = 30 - 1.5x; arranged to plot the graph (red)<BR>\n" );
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document.write( "The graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-10%2C+25%2C+-10%2C+30%2C+24-x%2C+30-1.5x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-10%2C+25%2C+-10%2C+30%2C+24-x%2C+30-1.5x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The 3 corners of the area of feasibility (at or below the lines whichever is lower):<BR>\n" );
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document.write( "..x/y;.....profit on each type;... total profit<BR>\n" );
document.write( " 0,24; 40(0) + 35(24) = 0 + 840 = $840<BR>\n" );
document.write( "12,12; 40(12) + 35(12) = 480 + 420 = $900<BR>\n" );
document.write( "20,0; 40(20) + 35(0) = 800 + 35(0) = $800<BR>\n" );
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document.write( "obviously 12 of each type would give max profit\r<BR>\n" );
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