document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202803>Question 1202803</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sally Sethness assembles stereo equipment for resale in her shop. She offers two products, turntables and cassette players. She makes a profit of $10 on each turntable and $6 on each cassette. Both must go through two steps in her shop—assembly and bench checking. A turntable takes 12 hours to assemble and 4 hours to bench check. A cassette player takes 4 hours to assemble but 8 hours to bench check. Looking at this month's schedule, Sally sees that she has 60 assembly hours uncommitted and 40 hours of bench-checking time available. Use graphic linear programming to find her best combination of turntables and cassette players. What is the total profit on the combination you found? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #837914 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=837914\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = number of turntables<BR>\n" );
document.write( "y = number of cassette players<BR>\n" );
document.write( "objecive function if profit.<BR>\n" );
document.write( "profit = 10x + 6y<BR>\n" );
document.write( "assembly constraints are:<BR>\n" );
document.write( "12x + 4y <= 60<BR>\n" );
document.write( "bench test constraints are:<BR>\n" );
document.write( "4x + 8y <= 40<BR>\n" );
document.write( "x >= 0<BR>\n" );
document.write( "y >= 0<BR>\n" );
document.write( "using the desmos.com calculator, you would graph the opposite of the constraints.<BR>\n" );
document.write( "the area not shaded is the region of feasibility.<BR>\n" );
document.write( "you would then evaluate the profit at the corner points of this feasible region to find the corner point with the maximum profit.\r<BR>\n" );
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document.write( "corner points are (0,5), (4,3), (5,0).<BR>\n" );
document.write( "maximum profit is 58 at (4,3)<BR>\n" );
document.write( "all constraints are satisfied at that point, as they need to be.\r<BR>\n" );
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document.write( "desmos.com calculator is at <a  rel=nofollow HREF= \"https://www.desmos.com/calculator\" target = \"_blank\">https://www.desmos.com/calculator</a>\r<BR>\n" );
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document.write( "here's what the graph looks like.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/061801.jpg\">\r<BR>\n" );
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document.write( " </SPAN>\n" );
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