document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1123606>Question 1123606</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The manufacturer of dolls want to maximize their revenue for the sale of the dolls. Each girl doll sold yields $9 in revenue and each boy doll yields $9.50. The dolls are made of plastic and nylon. To make a girl doll requires 12 oz of plastic and 5 oz of nylon. A boy doll requires 14oz of plastic but no nylon. The manufacturer has no more than 100,000 oz of plastic and 30,000o of nylon available each week. Kids will buy at least twice as many girl dolls as boys. How many of each should they manufacture each week to maximize their revenue? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #739964 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=739964\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your objective function is 9x + 9.5y which you want to minimize.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your constraint functions are:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "12x + 4y <= 400,00 (plastic constraint)<BR>\n" );
document.write( "5x <= 30,000 (silk constraint)<BR>\n" );
document.write( "x,y >= 0 (can't be negative)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "using the desmos.com calculator, you would graph the opposite of these constraints.<BR>\n" );
document.write( "the area of the graph that is not shaded is your region of feasibility.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the corner points of this region are where the maximum revenue will be.<BR>\n" );
document.write( "you will evaluts the objective function at these corner points to determine thye corner point that provides the most revenue.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you also need to confirm that all constraints are satisfied as the corner point with the maximum revenue.\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/2018/091901.jpg\" alt=\"$$$\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the corner point with the maximum revenue is at (6000,2000)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the revenue at this corner point was 73,000, which was higher than at any of the other corner points.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the plastic consumed was 100,000 and the nylon consumed was 30,000, all under the constraint limits of <= 100,000 and <= 30,000.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the cost function at the corner point was 9 * 6,000 + 9.5 * 2000 = 73,000\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the plastic constraint was 12 * 6000 + 14 * 2000 = 100,000\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the nylon constraint was 5 * 6000 + 0 * 2000 = 30,000\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the desmos.com calculator can be found at <a  rel=nofollow HREF= \"https://www.desmos.com/calculator\" target = \"_blank\">https://www.desmos.com/calculator</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<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" );