document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1177950>Question 1177950</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A manufacturer of downhill and cross-country skis reports that manufacturing time is 3 hours and 7 hours, respectively, per ski and that finishing time is 2 hours for each downhill and 2 hours for each cross-crountry ski. There are only 35 hours per week available for the manufacturing process and 18 hours for the finishing process. The average profit is $62 for downhill ski and $63 for cross-country ski. The manufacturer wants to know how many of each type of ski should be made to maximize the weekly profit.\r<BR>\n" );
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document.write( "What are the corner points of the feasible region?\r<BR>\n" );
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document.write( "I tried solving and got the equations below, but I can't figure out why my vertices are not coming out right.<BR>\n" );
document.write( "3x+7y greater than or equal to sign 35<BR>\n" );
document.write( "2x+2y greater than or equal to sign 18<BR>\n" );
document.write( "I used (0,0) as test points for both and got (0,5) and (11.6,0) for one and (0,9) and (9,0) for the other. my vertices for the feasible region came out to (11.6, 0), (7,2), and (0,9). The (7,2) had a value of 560 when I typed it into my objective function of 62x+63y=z. Any help you can provide would be greatly appreciated.  \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #807111 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=807111\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B7y+%3C=35 ALIGN=MIDDLE  ALT=\"3x%2B7y+%3C=35\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B2y+%3C=+18 ALIGN=MIDDLE  ALT=\"2x%2B2y+%3C=+18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------solve this system and find intersection point\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B7y+%3C=35 ALIGN=MIDDLE  ALT=\"3x%2B7y+%3C=35\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7y+%3C=35-3x ALIGN=MIDDLE  ALT=\"7y+%3C=35-3x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3C=35%2F7-3x%2F7 ALIGN=MIDDLE  ALT=\"y+%3C=35%2F7-3x%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3C=5-3x%2F7 ALIGN=MIDDLE  ALT=\"y+%3C=5-3x%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >...........eq.1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B2y+%3C=+18 ALIGN=MIDDLE  ALT=\"2x%2B2y+%3C=+18\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......divide dy <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By+%3C=+9 ALIGN=MIDDLE  ALT=\"x%2By+%3C=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3C=+9-x ALIGN=MIDDLE  ALT=\"y+%3C=+9-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >...........eq.2\r<BR>\n" );
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document.write( "equal ight sides in eq.1 and eq.2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5-3x%2F7=9-x ALIGN=MIDDLE  ALT=\"5-3x%2F7=9-x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3x%2F7=9-5 ALIGN=MIDDLE  ALT=\"x-3x%2F7=9-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287x-3x%29%2F7=4 ALIGN=MIDDLE  ALT=\"%287x-3x%29%2F7=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x-3x=4%2A7 ALIGN=MIDDLE  ALT=\"7x-3x=4%2A7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x=4%2A7 ALIGN=MIDDLE  ALT=\"4x=4%2A7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28cross%284%29%2A7%29%2Fcross%284%29 ALIGN=MIDDLE  ALT=\"x=%28cross%284%29%2A7%29%2Fcross%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3C=+9-x ALIGN=MIDDLE  ALT=\"y+%3C=+9-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >... substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3C=+9-7 ALIGN=MIDDLE  ALT=\"y+%3C=+9-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3C=+2 ALIGN=MIDDLE  ALT=\"y+%3C=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "intersection point is: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "profit is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=62x%2B63y ALIGN=MIDDLE  ALT=\"P=62x%2B63y\"   DISABLED_style= \"max-width:90%; height:auto;\" >....substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=62%2A7%2B63%2A2 ALIGN=MIDDLE  ALT=\"P=62%2A7%2B63%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=560 ALIGN=MIDDLE  ALT=\"P=560\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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