document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1175827>Question 1175827</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A computer store sells two types of laptops, an all-purpose laptop and a gaming laptop. The supplier demands that at least 150 of these laptops be sold each month. Experience shows that most consumers prefer all-purpose laptops, but some younger consumers prefer gaming laptops. The result is that the number of all-purpose laptops sold is at least twice the number of gaming laptops sold. The store pays its sales staff a $43.27 commission for each all-purpose laptop sold and a $49.73 commission for each gaming laptop sold. How many of each type of laptop should be sold to minimize commission? What is that minimum monthly commission?\r<BR>\n" );
document.write( "\n" );
document.write( "All-purpose laptops:	<BR>\n" );
document.write( "Gaming laptops:	<BR>\n" );
document.write( "Commission (dollars): </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #801539 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=801539\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = number of all purpose computers and y = number of gaming computers.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your objective function is commision = 43.27 * x + 49.73 * y\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is what you want to minimize.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your constraints are:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x + y >= 150<BR>\n" );
document.write( "x >= 2 * y<BR>\n" );
document.write( "x >= 0<BR>\n" );
document.write( "y >= 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "using the desmos.com calculator, graph the opposite of the inequalities.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the unshaded area of the graph is the region of feasibility.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your minimum commission will be at the corner points of the feasible region.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the graph looks like this.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/022501.jpg\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "from the graph, it looks like there are 2 corner points.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "at x = 100 and y = 50, the commission is equal to 6813.5<BR>\n" );
document.write( "at x = 150 and y = 0, the commission is equal to 6390.5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the least commission is paid when the number of general purpose laptops sold is 150 and the number of gaming laptops sold is 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you are evaluating the objective function at each of the corner points.<BR>\n" );
document.write( "all the constraints need to be saisfied as well.<BR>\n" );
document.write( "for example:<BR>\n" );
document.write( "at x = 100 and y = 50, the objective function is 100 * 43.27 + 50 * 49.73 = 6813.5<BR>\n" );
document.write( "the constraints of x >= 0 and y >= 0 are satisfied.<BR>\n" );
document.write( "the constraints of x + y >= 150 are also satisfied.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );